Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
Groups > sci.math > #641055 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2025-11-24 18:53 -0600 |
| Last post | 2025-12-05 17:45 -0600 |
| Articles | 20 on this page of 115 — 9 participants |
Back to article view | Back to sci.math
A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-24 18:53 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-25 11:40 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-25 08:21 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-26 13:37 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 09:39 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-26 12:44 -0500
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-27 09:56 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-27 09:31 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:58 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 09:51 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-28 11:04 -0500
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-29 12:17 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 11:54 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:22 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 09:54 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-26 12:49 -0500
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:43 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 14:04 -0600
Re: A new foundation for correct reasoning Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 21:42 +0000
Re: A new foundation for correct reasoning Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 21:49 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 15:54 -0600
Re: A new foundation for correct reasoning "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:33 -0800
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 15:50 -0600
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 11:26 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-02 07:22 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-27 10:00 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-27 09:43 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-28 11:01 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 09:54 -0600
Re: A new foundation for correct reasoning Alan Mackenzie <acm@muc.de> - 2025-11-28 17:32 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 12:40 -0600
Re: A new foundation for correct reasoning Alan Mackenzie <acm@muc.de> - 2025-11-28 18:51 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 13:21 -0600
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 08:43 -0600
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 19:59 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-28 16:49 -0500
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 20:07 -0600
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 20:30 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-29 12:20 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 11:57 -0600
Re: A new foundation for correct reasoning Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-29 11:27 -0800
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 13:33 -0600
Re: A new foundation for correct reasoning Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-30 10:33 -0800
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:58 +0200
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-04 02:32 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 20:39 -0600
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-04 08:06 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:38 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 11:43 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:30 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-06 06:50 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-07 13:02 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-08 13:49 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-08 11:13 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-08 13:09 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-10 12:04 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 08:10 -0600
Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-10 15:01 +0000
Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-10 15:03 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 10:14 -0600
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-10 18:10 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 14:01 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-11 10:42 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-11 08:17 -0600
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-11 23:28 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-11 17:49 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-11 19:52 -0500
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-12 10:50 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-12 08:19 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-12 09:24 -0500
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-14 19:03 +0000
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-13 12:19 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-13 08:43 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-13 13:36 -0500
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-14 12:05 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 17:14 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 19:13 -0500
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 18:46 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 19:53 -0500
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 19:08 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 20:46 -0500
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 20:05 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 21:23 -0500
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 20:09 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 21:27 -0500
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 21:22 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-15 07:33 -0500
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-15 11:04 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-15 08:03 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-16 11:44 +0200
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-16 11:48 +0200
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-05 10:49 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 11:05 -0600
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-06 08:24 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-06 06:08 -0600
Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-06 13:03 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-06 07:14 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-08 11:18 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-08 13:12 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-10 12:10 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 10:29 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-11 10:40 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-11 08:15 -0600
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-12 10:46 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-12 08:16 -0600
Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-12 09:22 -0500
Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-13 12:42 +0200
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-13 09:37 -0600
Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-13 15:42 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 11:00 -0600
Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-05 22:17 +0000
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 16:24 -0600
Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-05 22:45 +0000
Re: A new foundation for correct reasoning Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-12-05 15:16 -0800
Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 17:45 -0600
Page 1 of 6 [1] 2 3 4 5 6 Next page →
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-24 18:53 -0600 |
| Subject | A new foundation for correct reasoning |
| Message-ID | <10g2umt$2vnfa$1@dont-email.me> |
Eliminating undecidability and mathematical incompleteness merely requires discarding model theory and fully integrating semantics directly into the syntax of the formal language. The only inference step allowed is semantic logical entailment and this is performed syntactically. A formal language such as Montague Grammar or CycL of the Cyc project can encode the semantics of anything that can be expressed in language. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable.
[toc] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-25 11:40 +0200 |
| Message-ID | <10g3tj8$39v8g$1@dont-email.me> |
| In reply to | #641055 |
olcott kirjoitti 25.11.2025 klo 2.53: > Eliminating undecidability and mathematical incompleteness > merely requires discarding model theory and fully integrating > semantics directly into the syntax of the formal language. > > The only inference step allowed is semantic logical > entailment and this is performed syntactically. A formal > language such as Montague Grammar or CycL of the Cyc > project can encode the semantics of anything that can > be expressed in language. The resulting theory is not formal unless both the definition of semantics and the definition of semantic logical entailment are fully formal. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 08:21 -0600 |
| Message-ID | <10g4e1v$3ggnk$1@dont-email.me> |
| In reply to | #641059 |
On 11/25/2025 3:40 AM, Mikko wrote: > olcott kirjoitti 25.11.2025 klo 2.53: >> Eliminating undecidability and mathematical incompleteness >> merely requires discarding model theory and fully integrating >> semantics directly into the syntax of the formal language. >> >> The only inference step allowed is semantic logical >> entailment and this is performed syntactically. A formal >> language such as Montague Grammar or CycL of the Cyc >> project can encode the semantics of anything that can >> be expressed in language. > > The resulting theory is not formal unless both the definition of > semantics and the definition of semantic logical entailment are > fully formal. > > https://plato.stanford.edu/entries/montague-semantics/ https://en.wikipedia.org/wiki/CycL https://en.wikipedia.org/wiki/Ontology_(information_science) *This was my original inspiration* Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote: By the theory of simple types I mean the doctrine which says that the objects of thought (or, in another interpretation, the symbolic expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations, etc. (with a similar hierarchy for extensions), and that sentences of the form: " a has the property φ ", " b bears the relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable.
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-26 13:37 +0200 |
| Message-ID | <10g6op4$ber5$1@dont-email.me> |
| In reply to | #641063 |
olcott kirjoitti 25.11.2025 klo 16.21: > On 11/25/2025 3:40 AM, Mikko wrote: >> olcott kirjoitti 25.11.2025 klo 2.53: >>> Eliminating undecidability and mathematical incompleteness >>> merely requires discarding model theory and fully integrating >>> semantics directly into the syntax of the formal language. >>> >>> The only inference step allowed is semantic logical >>> entailment and this is performed syntactically. A formal >>> language such as Montague Grammar or CycL of the Cyc >>> project can encode the semantics of anything that can >>> be expressed in language. >> >> The resulting theory is not formal unless both the definition of >> semantics and the definition of semantic logical entailment are >> fully formal. >> >> > > https://plato.stanford.edu/entries/montague-semantics/ > https://en.wikipedia.org/wiki/CycL > https://en.wikipedia.org/wiki/Ontology_(information_science) > > *This was my original inspiration* > Kurt Gödel in his 1944 Russell's mathematical logic gave the following > definition of the "theory of simple types" in a footnote: > > By the theory of simple types I mean the doctrine which says that the > objects of thought (or, in another interpretation, the symbolic > expressions) are divided into types, namely: individuals, properties of > individuals, relations between individuals, properties of such > relations, etc. (with a similar hierarchy for extensions), and that > sentences of the form: " a has the property φ ", " b bears the relation > R to c ", etc. are meaningless, if a, b, c, R, φ are not of types > fitting together. That is a constraint on the language. Note that individuals of all sorts are considered to be of the same type. For properies and relation the alternative would be that a predicate is false if any of the arguments are of wrong type. For functions it is harder to find a reasonable value if an argument is of wrong type. This is of course irrelevant to the point that the resulting theory is not formal unless both the definition of semantics and the definition of semantic logical entailment are fully formal. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-26 09:39 -0600 |
| Message-ID | <10g76us$h4u7$1@dont-email.me> |
| In reply to | #641200 |
On 11/26/2025 5:37 AM, Mikko wrote: > olcott kirjoitti 25.11.2025 klo 16.21: >> On 11/25/2025 3:40 AM, Mikko wrote: >>> olcott kirjoitti 25.11.2025 klo 2.53: >>>> Eliminating undecidability and mathematical incompleteness >>>> merely requires discarding model theory and fully integrating >>>> semantics directly into the syntax of the formal language. >>>> >>>> The only inference step allowed is semantic logical >>>> entailment and this is performed syntactically. A formal >>>> language such as Montague Grammar or CycL of the Cyc >>>> project can encode the semantics of anything that can >>>> be expressed in language. >>> >>> The resulting theory is not formal unless both the definition of >>> semantics and the definition of semantic logical entailment are >>> fully formal. >>> >>> >> >> https://plato.stanford.edu/entries/montague-semantics/ >> https://en.wikipedia.org/wiki/CycL >> https://en.wikipedia.org/wiki/Ontology_(information_science) >> >> *This was my original inspiration* >> Kurt Gödel in his 1944 Russell's mathematical logic gave the following >> definition of the "theory of simple types" in a footnote: >> >> By the theory of simple types I mean the doctrine which says that the >> objects of thought (or, in another interpretation, the symbolic >> expressions) are divided into types, namely: individuals, properties >> of individuals, relations between individuals, properties of such >> relations, etc. (with a similar hierarchy for extensions), and that >> sentences of the form: " a has the property φ ", " b bears the >> relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of >> types fitting together. > > That is a constraint on the language. Note that individuals of all sorts > are considered to be of the same type. For properies and relation the > alternative would be that a predicate is false if any of the arguments > are of wrong type. For functions it is harder to find a reasonable value > if an argument is of wrong type. > > This is of course irrelevant to the point that the resulting theory is > not formal unless both the definition of semantics and the definition of > semantic logical entailment are fully formal. > The body of knowledge is defined in terms of Rudolf Carnap Meaning Postulates and stored in a knowledge ontology inheritance hierarchy. The predicate Bachelor(x) is stipulated to mean ~Married(x) where the predicate Married(x) is defined in terms of billions of other things such as all of the details of Human(x). -- 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.
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-26 12:44 -0500 |
| Message-ID | <60HVQ.49149$r_jb.46295@fx11.iad> |
| In reply to | #641219 |
On 11/26/25 10:39 AM, olcott wrote: > On 11/26/2025 5:37 AM, Mikko wrote: >> olcott kirjoitti 25.11.2025 klo 16.21: >>> On 11/25/2025 3:40 AM, Mikko wrote: >>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>> Eliminating undecidability and mathematical incompleteness >>>>> merely requires discarding model theory and fully integrating >>>>> semantics directly into the syntax of the formal language. >>>>> >>>>> The only inference step allowed is semantic logical >>>>> entailment and this is performed syntactically. A formal >>>>> language such as Montague Grammar or CycL of the Cyc >>>>> project can encode the semantics of anything that can >>>>> be expressed in language. >>>> >>>> The resulting theory is not formal unless both the definition of >>>> semantics and the definition of semantic logical entailment are >>>> fully formal. >>>> >>>> >>> >>> https://plato.stanford.edu/entries/montague-semantics/ >>> https://en.wikipedia.org/wiki/CycL >>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>> >>> *This was my original inspiration* >>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>> following definition of the "theory of simple types" in a footnote: >>> >>> By the theory of simple types I mean the doctrine which says that the >>> objects of thought (or, in another interpretation, the symbolic >>> expressions) are divided into types, namely: individuals, properties >>> of individuals, relations between individuals, properties of such >>> relations, etc. (with a similar hierarchy for extensions), and that >>> sentences of the form: " a has the property φ ", " b bears the >>> relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of >>> types fitting together. >> >> That is a constraint on the language. Note that individuals of all sorts >> are considered to be of the same type. For properies and relation the >> alternative would be that a predicate is false if any of the arguments >> are of wrong type. For functions it is harder to find a reasonable value >> if an argument is of wrong type. >> >> This is of course irrelevant to the point that the resulting theory is >> not formal unless both the definition of semantics and the definition of >> semantic logical entailment are fully formal. >> > > The body of knowledge is defined in terms of Rudolf Carnap Meaning > Postulates and stored in a knowledge ontology inheritance hierarchy. > > The predicate Bachelor(x) is stipulated to mean ~Married(x) where the > predicate Married(x) is defined in terms of billions of other things > such as all of the details of Human(x). > IN *YOUR* system, but not in his. All you are doing is admitting you don't beleive in keeping sematics, but think lying by changing meaning is valid. Of course, it seems you are too brain dead to understand what that means.
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-27 09:56 +0200 |
| Message-ID | <10g908c$16u06$1@dont-email.me> |
| In reply to | #641219 |
olcott kirjoitti 26.11.2025 klo 17.39: > On 11/26/2025 5:37 AM, Mikko wrote: >> olcott kirjoitti 25.11.2025 klo 16.21: >>> On 11/25/2025 3:40 AM, Mikko wrote: >>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>> Eliminating undecidability and mathematical incompleteness >>>>> merely requires discarding model theory and fully integrating >>>>> semantics directly into the syntax of the formal language. >>>>> >>>>> The only inference step allowed is semantic logical >>>>> entailment and this is performed syntactically. A formal >>>>> language such as Montague Grammar or CycL of the Cyc >>>>> project can encode the semantics of anything that can >>>>> be expressed in language. >>>> >>>> The resulting theory is not formal unless both the definition of >>>> semantics and the definition of semantic logical entailment are >>>> fully formal. >>>> >>>> >>> >>> https://plato.stanford.edu/entries/montague-semantics/ >>> https://en.wikipedia.org/wiki/CycL >>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>> >>> *This was my original inspiration* >>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>> following definition of the "theory of simple types" in a footnote: >>> >>> By the theory of simple types I mean the doctrine which says that the >>> objects of thought (or, in another interpretation, the symbolic >>> expressions) are divided into types, namely: individuals, properties >>> of individuals, relations between individuals, properties of such >>> relations, etc. (with a similar hierarchy for extensions), and that >>> sentences of the form: " a has the property φ ", " b bears the >>> relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of >>> types fitting together. >> >> That is a constraint on the language. Note that individuals of all sorts >> are considered to be of the same type. For properies and relation the >> alternative would be that a predicate is false if any of the arguments >> are of wrong type. For functions it is harder to find a reasonable value >> if an argument is of wrong type. >> >> This is of course irrelevant to the point that the resulting theory is >> not formal unless both the definition of semantics and the definition of >> semantic logical entailment are fully formal. > > The body of knowledge is defined in terms of Rudolf Carnap Meaning > Postulates and stored in a knowledge ontology inheritance hierarchy. > > The predicate Bachelor(x) is stipulated to mean ~Married(x) where the > predicate Married(x) is defined in terms of billions of other things > such as all of the details of Human(x). That, too, is irrelevant to the point that the resulting theory is not formal unless both the definition of semantics and the definition of semantic logical entailment are fully formal. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-27 09:31 -0600 |
| Message-ID | <10g9qtb$1hca0$1@dont-email.me> |
| In reply to | #641298 |
On 11/27/2025 1:56 AM, Mikko wrote: > olcott kirjoitti 26.11.2025 klo 17.39: >> On 11/26/2025 5:37 AM, Mikko wrote: >>> olcott kirjoitti 25.11.2025 klo 16.21: >>>> On 11/25/2025 3:40 AM, Mikko wrote: >>>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>>> Eliminating undecidability and mathematical incompleteness >>>>>> merely requires discarding model theory and fully integrating >>>>>> semantics directly into the syntax of the formal language. >>>>>> >>>>>> The only inference step allowed is semantic logical >>>>>> entailment and this is performed syntactically. A formal >>>>>> language such as Montague Grammar or CycL of the Cyc >>>>>> project can encode the semantics of anything that can >>>>>> be expressed in language. >>>>> >>>>> The resulting theory is not formal unless both the definition of >>>>> semantics and the definition of semantic logical entailment are >>>>> fully formal. >>>>> >>>>> >>>> >>>> https://plato.stanford.edu/entries/montague-semantics/ >>>> https://en.wikipedia.org/wiki/CycL >>>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>>> >>>> *This was my original inspiration* >>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>>> following definition of the "theory of simple types" in a footnote: >>>> >>>> By the theory of simple types I mean the doctrine which says that >>>> the objects of thought (or, in another interpretation, the symbolic >>>> expressions) are divided into types, namely: individuals, properties >>>> of individuals, relations between individuals, properties of such >>>> relations, etc. (with a similar hierarchy for extensions), and that >>>> sentences of the form: " a has the property φ ", " b bears the >>>> relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of >>>> types fitting together. >>> >>> That is a constraint on the language. Note that individuals of all sorts >>> are considered to be of the same type. For properies and relation the >>> alternative would be that a predicate is false if any of the arguments >>> are of wrong type. For functions it is harder to find a reasonable value >>> if an argument is of wrong type. >>> >>> This is of course irrelevant to the point that the resulting theory is >>> not formal unless both the definition of semantics and the definition of >>> semantic logical entailment are fully formal. >> >> The body of knowledge is defined in terms of Rudolf Carnap Meaning >> Postulates and stored in a knowledge ontology inheritance hierarchy. >> >> The predicate Bachelor(x) is stipulated to mean ~Married(x) where the >> predicate Married(x) is defined in terms of billions of other things >> such as all of the details of Human(x). > > That, too, is irrelevant to the point that the resulting theory is not > formal unless both the definition of semantics and the definition of > semantic logical entailment are fully formal. > In Olcott's Minimal Type Theory Rudolf Carnap Meaning Postulates directly encode semantic meaning in the syntax. The meaningless finite string "Bachelor" is defined as a semantic predicate through other already defined terms ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) Adapted by Olcott from Rudolf Carnap Meaning postulates. And encoded in the syntax of Olcott's Minimal Type Theory https://philarchive.org/archive/PETMTT-4v2 The predicate Human(x) requires trillions of other Meaning postulates to provide all of its semantic meaning. -- 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.
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-28 10:58 +0200 |
| Message-ID | <10gbo88$28ikt$1@dont-email.me> |
| In reply to | #641314 |
olcott kirjoitti 27.11.2025 klo 17.31: > On 11/27/2025 1:56 AM, Mikko wrote: >> olcott kirjoitti 26.11.2025 klo 17.39: >>> On 11/26/2025 5:37 AM, Mikko wrote: >>>> olcott kirjoitti 25.11.2025 klo 16.21: >>>>> On 11/25/2025 3:40 AM, Mikko wrote: >>>>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>>>> Eliminating undecidability and mathematical incompleteness >>>>>>> merely requires discarding model theory and fully integrating >>>>>>> semantics directly into the syntax of the formal language. >>>>>>> >>>>>>> The only inference step allowed is semantic logical >>>>>>> entailment and this is performed syntactically. A formal >>>>>>> language such as Montague Grammar or CycL of the Cyc >>>>>>> project can encode the semantics of anything that can >>>>>>> be expressed in language. >>>>>> >>>>>> The resulting theory is not formal unless both the definition of >>>>>> semantics and the definition of semantic logical entailment are >>>>>> fully formal. >>>>>> >>>>>> >>>>> >>>>> https://plato.stanford.edu/entries/montague-semantics/ >>>>> https://en.wikipedia.org/wiki/CycL >>>>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>>>> >>>>> *This was my original inspiration* >>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>>>> following definition of the "theory of simple types" in a footnote: >>>>> >>>>> By the theory of simple types I mean the doctrine which says that >>>>> the objects of thought (or, in another interpretation, the symbolic >>>>> expressions) are divided into types, namely: individuals, >>>>> properties of individuals, relations between individuals, >>>>> properties of such relations, etc. (with a similar hierarchy for >>>>> extensions), and that sentences of the form: " a has the property φ >>>>> ", " b bears the relation R to c ", etc. are meaningless, if a, b, >>>>> c, R, φ are not of types fitting together. >>>> >>>> That is a constraint on the language. Note that individuals of all >>>> sorts >>>> are considered to be of the same type. For properies and relation the >>>> alternative would be that a predicate is false if any of the arguments >>>> are of wrong type. For functions it is harder to find a reasonable >>>> value >>>> if an argument is of wrong type. >>>> >>>> This is of course irrelevant to the point that the resulting theory is >>>> not formal unless both the definition of semantics and the >>>> definition of >>>> semantic logical entailment are fully formal. >>> >>> The body of knowledge is defined in terms of Rudolf Carnap Meaning >>> Postulates and stored in a knowledge ontology inheritance hierarchy. >>> >>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where the >>> predicate Married(x) is defined in terms of billions of other things >>> such as all of the details of Human(x). >> >> That, too, is irrelevant to the point that the resulting theory is not >> formal unless both the definition of semantics and the definition of >> semantic logical entailment are fully formal. > In Olcott's Minimal Type Theory Rudolf Carnap Meaning > Postulates directly encode semantic meaning in the syntax. if the encoding is not fully formally specified the theory is not formal. > The meaningless finite string "Bachelor" is defined as > a semantic predicate through other already defined terms > ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) > Adapted by Olcott from Rudolf Carnap Meaning postulates. > > And encoded in the syntax of Olcott's Minimal Type Theory > https://philarchive.org/archive/PETMTT-4v2 That page only tells how to define a sentence in terms of other sentences. As it does not permit any arguments on the left side of := the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) is syntactically invalid. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-28 09:51 -0600 |
| Message-ID | <10gcgd9$2hrab$1@dont-email.me> |
| In reply to | #641333 |
On 11/28/2025 2:58 AM, Mikko wrote:
> olcott kirjoitti 27.11.2025 klo 17.31:
>> On 11/27/2025 1:56 AM, Mikko wrote:
>>> olcott kirjoitti 26.11.2025 klo 17.39:
>>>> On 11/26/2025 5:37 AM, Mikko wrote:
>>>>> olcott kirjoitti 25.11.2025 klo 16.21:
>>>>>> On 11/25/2025 3:40 AM, Mikko wrote:
>>>>>>> olcott kirjoitti 25.11.2025 klo 2.53:
>>>>>>>> Eliminating undecidability and mathematical incompleteness
>>>>>>>> merely requires discarding model theory and fully integrating
>>>>>>>> semantics directly into the syntax of the formal language.
>>>>>>>>
>>>>>>>> The only inference step allowed is semantic logical
>>>>>>>> entailment and this is performed syntactically. A formal
>>>>>>>> language such as Montague Grammar or CycL of the Cyc
>>>>>>>> project can encode the semantics of anything that can
>>>>>>>> be expressed in language.
>>>>>>>
>>>>>>> The resulting theory is not formal unless both the definition of
>>>>>>> semantics and the definition of semantic logical entailment are
>>>>>>> fully formal.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> https://plato.stanford.edu/entries/montague-semantics/
>>>>>> https://en.wikipedia.org/wiki/CycL
>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science)
>>>>>>
>>>>>> *This was my original inspiration*
>>>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the
>>>>>> following definition of the "theory of simple types" in a footnote:
>>>>>>
>>>>>> By the theory of simple types I mean the doctrine which says that
>>>>>> the objects of thought (or, in another interpretation, the
>>>>>> symbolic expressions) are divided into types, namely: individuals,
>>>>>> properties of individuals, relations between individuals,
>>>>>> properties of such relations, etc. (with a similar hierarchy for
>>>>>> extensions), and that sentences of the form: " a has the property
>>>>>> φ ", " b bears the relation R to c ", etc. are meaningless, if a,
>>>>>> b, c, R, φ are not of types fitting together.
>>>>>
>>>>> That is a constraint on the language. Note that individuals of all
>>>>> sorts
>>>>> are considered to be of the same type. For properies and relation the
>>>>> alternative would be that a predicate is false if any of the arguments
>>>>> are of wrong type. For functions it is harder to find a reasonable
>>>>> value
>>>>> if an argument is of wrong type.
>>>>>
>>>>> This is of course irrelevant to the point that the resulting theory is
>>>>> not formal unless both the definition of semantics and the
>>>>> definition of
>>>>> semantic logical entailment are fully formal.
>>>>
>>>> The body of knowledge is defined in terms of Rudolf Carnap Meaning
>>>> Postulates and stored in a knowledge ontology inheritance hierarchy.
>>>>
>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where
>>>> the predicate Married(x) is defined in terms of billions of other
>>>> things such as all of the details of Human(x).
>>>
>>> That, too, is irrelevant to the point that the resulting theory is not
>>> formal unless both the definition of semantics and the definition of
>>> semantic logical entailment are fully formal.
>
>> In Olcott's Minimal Type Theory Rudolf Carnap Meaning
>> Postulates directly encode semantic meaning in the syntax.
>
> if the encoding is not fully formally specified the theory is not
> formal.
>
>> The meaningless finite string "Bachelor" is defined as
>> a semantic predicate through other already defined terms
>> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))
>> Adapted by Olcott from Rudolf Carnap Meaning postulates.
>>
>> And encoded in the syntax of Olcott's Minimal Type Theory
>> https://philarchive.org/archive/PETMTT-4v2
>
> That page only tells how to define a sentence in terms of other
> sentences. As it does not permit any arguments on the left side of :=
> the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))
> is syntactically invalid.
>
∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x)))
<sentence_7 token="FOR_ALL">
<sentence_7 token="ELEMENT_OF">
<sentence_7 token="IDENTIFIER" value="x"/>
<sentence_7 token="IDENTIFIER" value="Human"/>
</sentence_7>
<sentence_11 token="IFF">
<atomic_sentence_1 token="IDENTIFIER" value="Bachelor">
<term_2 token="IDENTIFIER" value="x"/>
</atomic_sentence_1>
<sentence_12 token="AND">
<sentence_12 token="AND">
<atomic_sentence_1 token="IDENTIFIER" value="Male">
<term_2 token="IDENTIFIER" value="x"/>
</atomic_sentence_1>
<atomic_sentence_1 token="IDENTIFIER" value="Adult">
<term_2 token="IDENTIFIER" value="x"/>
</atomic_sentence_1>
</sentence_12>
<sentence_2 token="NOT">
<atomic_sentence_1 token="IDENTIFIER" value="Married">
<term_2 token="IDENTIFIER" value="x"/>
</atomic_sentence_1>
</sentence_2>
</sentence_12>
</sentence_11>
</sentence_7>
--
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.
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-28 11:04 -0500 |
| Message-ID | <JKjWQ.63584$C8i7.62818@fx16.iad> |
| In reply to | #641348 |
On 11/28/25 10:51 AM, olcott wrote: > On 11/28/2025 2:58 AM, Mikko wrote: >> olcott kirjoitti 27.11.2025 klo 17.31: >>> On 11/27/2025 1:56 AM, Mikko wrote: >>>> olcott kirjoitti 26.11.2025 klo 17.39: >>>>> On 11/26/2025 5:37 AM, Mikko wrote: >>>>>> olcott kirjoitti 25.11.2025 klo 16.21: >>>>>>> On 11/25/2025 3:40 AM, Mikko wrote: >>>>>>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>>>>>> Eliminating undecidability and mathematical incompleteness >>>>>>>>> merely requires discarding model theory and fully integrating >>>>>>>>> semantics directly into the syntax of the formal language. >>>>>>>>> >>>>>>>>> The only inference step allowed is semantic logical >>>>>>>>> entailment and this is performed syntactically. A formal >>>>>>>>> language such as Montague Grammar or CycL of the Cyc >>>>>>>>> project can encode the semantics of anything that can >>>>>>>>> be expressed in language. >>>>>>>> >>>>>>>> The resulting theory is not formal unless both the definition of >>>>>>>> semantics and the definition of semantic logical entailment are >>>>>>>> fully formal. >>>>>>>> >>>>>>>> >>>>>>> >>>>>>> https://plato.stanford.edu/entries/montague-semantics/ >>>>>>> https://en.wikipedia.org/wiki/CycL >>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>>>>>> >>>>>>> *This was my original inspiration* >>>>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>>>>>> following definition of the "theory of simple types" in a footnote: >>>>>>> >>>>>>> By the theory of simple types I mean the doctrine which says that >>>>>>> the objects of thought (or, in another interpretation, the >>>>>>> symbolic expressions) are divided into types, namely: >>>>>>> individuals, properties of individuals, relations between >>>>>>> individuals, properties of such relations, etc. (with a similar >>>>>>> hierarchy for extensions), and that sentences of the form: " a >>>>>>> has the property φ ", " b bears the relation R to c ", etc. are >>>>>>> meaningless, if a, b, c, R, φ are not of types fitting together. >>>>>> >>>>>> That is a constraint on the language. Note that individuals of all >>>>>> sorts >>>>>> are considered to be of the same type. For properies and relation the >>>>>> alternative would be that a predicate is false if any of the >>>>>> arguments >>>>>> are of wrong type. For functions it is harder to find a reasonable >>>>>> value >>>>>> if an argument is of wrong type. >>>>>> >>>>>> This is of course irrelevant to the point that the resulting >>>>>> theory is >>>>>> not formal unless both the definition of semantics and the >>>>>> definition of >>>>>> semantic logical entailment are fully formal. >>>>> >>>>> The body of knowledge is defined in terms of Rudolf Carnap Meaning >>>>> Postulates and stored in a knowledge ontology inheritance hierarchy. >>>>> >>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where >>>>> the predicate Married(x) is defined in terms of billions of other >>>>> things such as all of the details of Human(x). >>>> >>>> That, too, is irrelevant to the point that the resulting theory is not >>>> formal unless both the definition of semantics and the definition of >>>> semantic logical entailment are fully formal. >> >>> In Olcott's Minimal Type Theory Rudolf Carnap Meaning >>> Postulates directly encode semantic meaning in the syntax. >> >> if the encoding is not fully formally specified the theory is not >> formal. >> >>> The meaningless finite string "Bachelor" is defined as >>> a semantic predicate through other already defined terms >>> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) >>> Adapted by Olcott from Rudolf Carnap Meaning postulates. >>> >>> And encoded in the syntax of Olcott's Minimal Type Theory >>> https://philarchive.org/archive/PETMTT-4v2 >> >> That page only tells how to define a sentence in terms of other >> sentences. As it does not permit any arguments on the left side of := >> the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) >> is syntactically invalid. >> > > ∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x))) But that isn't the definition of Bachelor that he was talking about. You just don't understand the issue he was pointing out about Natural Language. > > <sentence_7 token="FOR_ALL"> > <sentence_7 token="ELEMENT_OF"> > <sentence_7 token="IDENTIFIER" value="x"/> > <sentence_7 token="IDENTIFIER" value="Human"/> > </sentence_7> > <sentence_11 token="IFF"> > <atomic_sentence_1 token="IDENTIFIER" value="Bachelor"> > <term_2 token="IDENTIFIER" value="x"/> > </atomic_sentence_1> > <sentence_12 token="AND"> > <sentence_12 token="AND"> > <atomic_sentence_1 token="IDENTIFIER" value="Male"> > <term_2 token="IDENTIFIER" value="x"/> > </atomic_sentence_1> > <atomic_sentence_1 token="IDENTIFIER" value="Adult"> > <term_2 token="IDENTIFIER" value="x"/> > </atomic_sentence_1> > </sentence_12> > <sentence_2 token="NOT"> > <atomic_sentence_1 token="IDENTIFIER" value="Married"> > <term_2 token="IDENTIFIER" value="x"/> > </atomic_sentence_1> > </sentence_2> > </sentence_12> > </sentence_11> > </sentence_7> > >
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-29 12:17 +0200 |
| Message-ID | <10geh87$38pe7$1@dont-email.me> |
| In reply to | #641348 |
olcott kirjoitti 28.11.2025 klo 17.51:
> On 11/28/2025 2:58 AM, Mikko wrote:
>> olcott kirjoitti 27.11.2025 klo 17.31:
>>> On 11/27/2025 1:56 AM, Mikko wrote:
>>>> olcott kirjoitti 26.11.2025 klo 17.39:
>>>>> On 11/26/2025 5:37 AM, Mikko wrote:
>>>>>> olcott kirjoitti 25.11.2025 klo 16.21:
>>>>>>> On 11/25/2025 3:40 AM, Mikko wrote:
>>>>>>>> olcott kirjoitti 25.11.2025 klo 2.53:
>>>>>>>>> Eliminating undecidability and mathematical incompleteness
>>>>>>>>> merely requires discarding model theory and fully integrating
>>>>>>>>> semantics directly into the syntax of the formal language.
>>>>>>>>>
>>>>>>>>> The only inference step allowed is semantic logical
>>>>>>>>> entailment and this is performed syntactically. A formal
>>>>>>>>> language such as Montague Grammar or CycL of the Cyc
>>>>>>>>> project can encode the semantics of anything that can
>>>>>>>>> be expressed in language.
>>>>>>>>
>>>>>>>> The resulting theory is not formal unless both the definition of
>>>>>>>> semantics and the definition of semantic logical entailment are
>>>>>>>> fully formal.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> https://plato.stanford.edu/entries/montague-semantics/
>>>>>>> https://en.wikipedia.org/wiki/CycL
>>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science)
>>>>>>>
>>>>>>> *This was my original inspiration*
>>>>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the
>>>>>>> following definition of the "theory of simple types" in a footnote:
>>>>>>>
>>>>>>> By the theory of simple types I mean the doctrine which says that
>>>>>>> the objects of thought (or, in another interpretation, the
>>>>>>> symbolic expressions) are divided into types, namely:
>>>>>>> individuals, properties of individuals, relations between
>>>>>>> individuals, properties of such relations, etc. (with a similar
>>>>>>> hierarchy for extensions), and that sentences of the form: " a
>>>>>>> has the property φ ", " b bears the relation R to c ", etc. are
>>>>>>> meaningless, if a, b, c, R, φ are not of types fitting together.
>>>>>>
>>>>>> That is a constraint on the language. Note that individuals of all
>>>>>> sorts
>>>>>> are considered to be of the same type. For properies and relation the
>>>>>> alternative would be that a predicate is false if any of the
>>>>>> arguments
>>>>>> are of wrong type. For functions it is harder to find a reasonable
>>>>>> value
>>>>>> if an argument is of wrong type.
>>>>>>
>>>>>> This is of course irrelevant to the point that the resulting
>>>>>> theory is
>>>>>> not formal unless both the definition of semantics and the
>>>>>> definition of
>>>>>> semantic logical entailment are fully formal.
>>>>>
>>>>> The body of knowledge is defined in terms of Rudolf Carnap Meaning
>>>>> Postulates and stored in a knowledge ontology inheritance hierarchy.
>>>>>
>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where
>>>>> the predicate Married(x) is defined in terms of billions of other
>>>>> things such as all of the details of Human(x).
>>>>
>>>> That, too, is irrelevant to the point that the resulting theory is not
>>>> formal unless both the definition of semantics and the definition of
>>>> semantic logical entailment are fully formal.
>>
>>> In Olcott's Minimal Type Theory Rudolf Carnap Meaning
>>> Postulates directly encode semantic meaning in the syntax.
>>
>> if the encoding is not fully formally specified the theory is not
>> formal.
>>
>>> The meaningless finite string "Bachelor" is defined as
>>> a semantic predicate through other already defined terms
>>> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))
>>> Adapted by Olcott from Rudolf Carnap Meaning postulates.
>>>
>>> And encoded in the syntax of Olcott's Minimal Type Theory
>>> https://philarchive.org/archive/PETMTT-4v2
>>
>> That page only tells how to define a sentence in terms of other
>> sentences. As it does not permit any arguments on the left side of :=
>> the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))
>> is syntactically invalid.
>
> ∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x)))
That is a different sentence. The syntax rules of
https://philarchive.org/archive/PETMTT-4v2
are different for := and =.
--
Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-29 11:54 -0600 |
| Message-ID | <10gfc03$3j8a6$1@dont-email.me> |
| In reply to | #641392 |
On 11/29/2025 4:17 AM, Mikko wrote: > olcott kirjoitti 28.11.2025 klo 17.51: >> On 11/28/2025 2:58 AM, Mikko wrote: >>> olcott kirjoitti 27.11.2025 klo 17.31: >>>> On 11/27/2025 1:56 AM, Mikko wrote: >>>>> olcott kirjoitti 26.11.2025 klo 17.39: >>>>>> On 11/26/2025 5:37 AM, Mikko wrote: >>>>>>> olcott kirjoitti 25.11.2025 klo 16.21: >>>>>>>> On 11/25/2025 3:40 AM, Mikko wrote: >>>>>>>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>>>>>>> Eliminating undecidability and mathematical incompleteness >>>>>>>>>> merely requires discarding model theory and fully integrating >>>>>>>>>> semantics directly into the syntax of the formal language. >>>>>>>>>> >>>>>>>>>> The only inference step allowed is semantic logical >>>>>>>>>> entailment and this is performed syntactically. A formal >>>>>>>>>> language such as Montague Grammar or CycL of the Cyc >>>>>>>>>> project can encode the semantics of anything that can >>>>>>>>>> be expressed in language. >>>>>>>>> >>>>>>>>> The resulting theory is not formal unless both the definition of >>>>>>>>> semantics and the definition of semantic logical entailment are >>>>>>>>> fully formal. >>>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>> https://plato.stanford.edu/entries/montague-semantics/ >>>>>>>> https://en.wikipedia.org/wiki/CycL >>>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>>>>>>> >>>>>>>> *This was my original inspiration* >>>>>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>>>>>>> following definition of the "theory of simple types" in a footnote: >>>>>>>> >>>>>>>> By the theory of simple types I mean the doctrine which says >>>>>>>> that the objects of thought (or, in another interpretation, the >>>>>>>> symbolic expressions) are divided into types, namely: >>>>>>>> individuals, properties of individuals, relations between >>>>>>>> individuals, properties of such relations, etc. (with a similar >>>>>>>> hierarchy for extensions), and that sentences of the form: " a >>>>>>>> has the property φ ", " b bears the relation R to c ", etc. are >>>>>>>> meaningless, if a, b, c, R, φ are not of types fitting together. >>>>>>> >>>>>>> That is a constraint on the language. Note that individuals of >>>>>>> all sorts >>>>>>> are considered to be of the same type. For properies and relation >>>>>>> the >>>>>>> alternative would be that a predicate is false if any of the >>>>>>> arguments >>>>>>> are of wrong type. For functions it is harder to find a >>>>>>> reasonable value >>>>>>> if an argument is of wrong type. >>>>>>> >>>>>>> This is of course irrelevant to the point that the resulting >>>>>>> theory is >>>>>>> not formal unless both the definition of semantics and the >>>>>>> definition of >>>>>>> semantic logical entailment are fully formal. >>>>>> >>>>>> The body of knowledge is defined in terms of Rudolf Carnap Meaning >>>>>> Postulates and stored in a knowledge ontology inheritance hierarchy. >>>>>> >>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where >>>>>> the predicate Married(x) is defined in terms of billions of other >>>>>> things such as all of the details of Human(x). >>>>> >>>>> That, too, is irrelevant to the point that the resulting theory is not >>>>> formal unless both the definition of semantics and the definition of >>>>> semantic logical entailment are fully formal. >>> >>>> In Olcott's Minimal Type Theory Rudolf Carnap Meaning >>>> Postulates directly encode semantic meaning in the syntax. >>> >>> if the encoding is not fully formally specified the theory is not >>> formal. >>> >>>> The meaningless finite string "Bachelor" is defined as >>>> a semantic predicate through other already defined terms >>>> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) >>>> Adapted by Olcott from Rudolf Carnap Meaning postulates. >>>> >>>> And encoded in the syntax of Olcott's Minimal Type Theory >>>> https://philarchive.org/archive/PETMTT-4v2 >>> >>> That page only tells how to define a sentence in terms of other >>> sentences. As it does not permit any arguments on the left side of := >>> the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) >>> is syntactically invalid. >> >> ∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x))) > > That is a different sentence. The syntax rules of > https://philarchive.org/archive/PETMTT-4v2 > are different for := and =. > It is equivalent. The term Bachelor(x) is still defined by Male(x) ∧ Adult(x) ∧ ~Married(x) ∧ Human(x) thus never circular at all as Willard Van Orman Quine insisted. -- 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.
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-30 11:22 +0200 |
| Message-ID | <10gh2bq$72q1$1@dont-email.me> |
| In reply to | #641413 |
olcott kirjoitti 29.11.2025 klo 19.54: > On 11/29/2025 4:17 AM, Mikko wrote: >> olcott kirjoitti 28.11.2025 klo 17.51: >>> On 11/28/2025 2:58 AM, Mikko wrote: >>>> olcott kirjoitti 27.11.2025 klo 17.31: >>>>> On 11/27/2025 1:56 AM, Mikko wrote: >>>>>> olcott kirjoitti 26.11.2025 klo 17.39: >>>>>>> On 11/26/2025 5:37 AM, Mikko wrote: >>>>>>>> olcott kirjoitti 25.11.2025 klo 16.21: >>>>>>>>> On 11/25/2025 3:40 AM, Mikko wrote: >>>>>>>>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>>>>>>>> Eliminating undecidability and mathematical incompleteness >>>>>>>>>>> merely requires discarding model theory and fully integrating >>>>>>>>>>> semantics directly into the syntax of the formal language. >>>>>>>>>>> >>>>>>>>>>> The only inference step allowed is semantic logical >>>>>>>>>>> entailment and this is performed syntactically. A formal >>>>>>>>>>> language such as Montague Grammar or CycL of the Cyc >>>>>>>>>>> project can encode the semantics of anything that can >>>>>>>>>>> be expressed in language. >>>>>>>>>> >>>>>>>>>> The resulting theory is not formal unless both the definition of >>>>>>>>>> semantics and the definition of semantic logical entailment are >>>>>>>>>> fully formal. >>>>>>>>>> >>>>>>>>>> >>>>>>>>> >>>>>>>>> https://plato.stanford.edu/entries/montague-semantics/ >>>>>>>>> https://en.wikipedia.org/wiki/CycL >>>>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>>>>>>>> >>>>>>>>> *This was my original inspiration* >>>>>>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>>>>>>>> following definition of the "theory of simple types" in a >>>>>>>>> footnote: >>>>>>>>> >>>>>>>>> By the theory of simple types I mean the doctrine which says >>>>>>>>> that the objects of thought (or, in another interpretation, the >>>>>>>>> symbolic expressions) are divided into types, namely: >>>>>>>>> individuals, properties of individuals, relations between >>>>>>>>> individuals, properties of such relations, etc. (with a similar >>>>>>>>> hierarchy for extensions), and that sentences of the form: " a >>>>>>>>> has the property φ ", " b bears the relation R to c ", etc. are >>>>>>>>> meaningless, if a, b, c, R, φ are not of types fitting together. >>>>>>>> >>>>>>>> That is a constraint on the language. Note that individuals of >>>>>>>> all sorts >>>>>>>> are considered to be of the same type. For properies and >>>>>>>> relation the >>>>>>>> alternative would be that a predicate is false if any of the >>>>>>>> arguments >>>>>>>> are of wrong type. For functions it is harder to find a >>>>>>>> reasonable value >>>>>>>> if an argument is of wrong type. >>>>>>>> >>>>>>>> This is of course irrelevant to the point that the resulting >>>>>>>> theory is >>>>>>>> not formal unless both the definition of semantics and the >>>>>>>> definition of >>>>>>>> semantic logical entailment are fully formal. >>>>>>> >>>>>>> The body of knowledge is defined in terms of Rudolf Carnap >>>>>>> Meaning Postulates and stored in a knowledge ontology inheritance >>>>>>> hierarchy. >>>>>>> >>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where >>>>>>> the predicate Married(x) is defined in terms of billions of other >>>>>>> things such as all of the details of Human(x). >>>>>> >>>>>> That, too, is irrelevant to the point that the resulting theory is >>>>>> not >>>>>> formal unless both the definition of semantics and the definition of >>>>>> semantic logical entailment are fully formal. >>>> >>>>> In Olcott's Minimal Type Theory Rudolf Carnap Meaning >>>>> Postulates directly encode semantic meaning in the syntax. >>>> >>>> if the encoding is not fully formally specified the theory is not >>>> formal. >>>> >>>>> The meaningless finite string "Bachelor" is defined as >>>>> a semantic predicate through other already defined terms >>>>> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) >>>>> Adapted by Olcott from Rudolf Carnap Meaning postulates. >>>>> >>>>> And encoded in the syntax of Olcott's Minimal Type Theory >>>>> https://philarchive.org/archive/PETMTT-4v2 >>>> >>>> That page only tells how to define a sentence in terms of other >>>> sentences. As it does not permit any arguments on the left side of := >>>> the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x))) >>>> is syntactically invalid. >>> >>> ∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x))) >> >> That is a different sentence. The syntax rules of >> https://philarchive.org/archive/PETMTT-4v2 >> are different for := and =. > > It is equivalent. The term Bachelor(x) is still defined by > Male(x) ∧ Adult(x) ∧ ~Married(x) ∧ Human(x) thus never > circular at all as Willard Van Orman Quine insisted. It is not equivalent. The one with ↔ merely claims it without saying why that is claimed. It may be a consequence of earlier assumtions or a new assumtion or a part of a quesstion. It cannot be a definition or a consequence of earlier definitions because MTT does not permit a definition of Bachelor, Male, Adult, or Married, or any other predicate. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-26 09:54 -0600 |
| Message-ID | <10g77rn$hh1c$1@dont-email.me> |
| In reply to | #641200 |
On 11/26/2025 5:37 AM, Mikko wrote: > olcott kirjoitti 25.11.2025 klo 16.21: >> On 11/25/2025 3:40 AM, Mikko wrote: >>> olcott kirjoitti 25.11.2025 klo 2.53: >>>> Eliminating undecidability and mathematical incompleteness >>>> merely requires discarding model theory and fully integrating >>>> semantics directly into the syntax of the formal language. >>>> >>>> The only inference step allowed is semantic logical >>>> entailment and this is performed syntactically. A formal >>>> language such as Montague Grammar or CycL of the Cyc >>>> project can encode the semantics of anything that can >>>> be expressed in language. >>> >>> The resulting theory is not formal unless both the definition of >>> semantics and the definition of semantic logical entailment are >>> fully formal. >>> >>> >> >> https://plato.stanford.edu/entries/montague-semantics/ >> https://en.wikipedia.org/wiki/CycL >> https://en.wikipedia.org/wiki/Ontology_(information_science) >> >> *This was my original inspiration* >> Kurt Gödel in his 1944 Russell's mathematical logic gave the following >> definition of the "theory of simple types" in a footnote: >> >> By the theory of simple types I mean the doctrine which says that the >> objects of thought (or, in another interpretation, the symbolic >> expressions) are divided into types, namely: individuals, properties >> of individuals, relations between individuals, properties of such >> relations, etc. (with a similar hierarchy for extensions), and that >> sentences of the form: " a has the property φ ", " b bears the >> relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of >> types fitting together. > > That is a constraint on the language. Note that individuals of all sorts > are considered to be of the same type. An individual house, person, orange, piece of pie, is not a group of houses, people, oranges, pieces of pie. > For properies and relation the > alternative would be that a predicate is false if any of the arguments > are of wrong type. For functions it is harder to find a reasonable value > if an argument is of wrong type. > (General_Knowledge ⊨ x) means True(x) (General_Knowledge ⊨ ~x) means False(x) ~True(x) & ~False(x) means x is not an element of General_Knowledge > This is of course irrelevant to the point that the resulting theory is > not formal unless both the definition of semantics and the definition of > semantic logical entailment are fully formal. > -- 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.
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-26 12:49 -0500 |
| Message-ID | <%4HVQ.46063$5c64.9249@fx10.iad> |
| In reply to | #641220 |
On 11/26/25 10:54 AM, olcott wrote: > On 11/26/2025 5:37 AM, Mikko wrote: >> olcott kirjoitti 25.11.2025 klo 16.21: >>> On 11/25/2025 3:40 AM, Mikko wrote: >>>> olcott kirjoitti 25.11.2025 klo 2.53: >>>>> Eliminating undecidability and mathematical incompleteness >>>>> merely requires discarding model theory and fully integrating >>>>> semantics directly into the syntax of the formal language. >>>>> >>>>> The only inference step allowed is semantic logical >>>>> entailment and this is performed syntactically. A formal >>>>> language such as Montague Grammar or CycL of the Cyc >>>>> project can encode the semantics of anything that can >>>>> be expressed in language. >>>> >>>> The resulting theory is not formal unless both the definition of >>>> semantics and the definition of semantic logical entailment are >>>> fully formal. >>>> >>>> >>> >>> https://plato.stanford.edu/entries/montague-semantics/ >>> https://en.wikipedia.org/wiki/CycL >>> https://en.wikipedia.org/wiki/Ontology_(information_science) >>> >>> *This was my original inspiration* >>> Kurt Gödel in his 1944 Russell's mathematical logic gave the >>> following definition of the "theory of simple types" in a footnote: >>> >>> By the theory of simple types I mean the doctrine which says that the >>> objects of thought (or, in another interpretation, the symbolic >>> expressions) are divided into types, namely: individuals, properties >>> of individuals, relations between individuals, properties of such >>> relations, etc. (with a similar hierarchy for extensions), and that >>> sentences of the form: " a has the property φ ", " b bears the >>> relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of >>> types fitting together. >> >> That is a constraint on the language. Note that individuals of all sorts >> are considered to be of the same type. > > An individual house, person, orange, piece of pie, > is not a group of houses, people, oranges, pieces of pie. > >> For properies and relation the >> alternative would be that a predicate is false if any of the arguments >> are of wrong type. For functions it is harder to find a reasonable value >> if an argument is of wrong type. >> > > (General_Knowledge ⊨ x) means True(x) Wrong. > (General_Knowledge ⊨ ~x) means False(x) Wrong. > ~True(x) & ~False(x) means x is not an element of General_Knowledge WHich means your definition of True and False are just LIES that don't match what logic defines them as. In your logic, the value of ~True is NOT False, but must stay as Not True, as the proposition might not have a knowable value. Try working in a system that can't take negations of logical results. It is a provable fact that for most of the great unsolved mathematical puzzle, they ARE either True or False, as either there exist a specific case where the proposition fails, or their doesn't. But you logic can't deal with that, because it is just an utterly broken system. > >> This is of course irrelevant to the point that the resulting theory is >> not formal unless both the definition of semantics and the definition of >> semantic logical entailment are fully formal. >> > > >
[toc] | [prev] | [next] | [standalone]
| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2025-11-26 19:43 +0000 |
| Message-ID | <10g7l8j$n6g7$1@dont-email.me> |
| In reply to | #641220 |
On 26/11/2025 15:54, olcott wrote: > (General_Knowledge ⊨ x) means True(x) > (General_Knowledge ⊨ ~x) means False(x) > ~True(x) & ~False(x) means x is not an element of General_Knowledge Eh? You made it sound like General_Knowledge was the system, rather than a model, but there you have it as a model. -- Tristan Wibberley The message body is Copyright (C) 2025 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-26 14:04 -0600 |
| Message-ID | <10g7mfk$nqtg$1@dont-email.me> |
| In reply to | #641237 |
On 11/26/2025 1:43 PM, Tristan Wibberley wrote: > On 26/11/2025 15:54, olcott wrote: >> (General_Knowledge ⊨ x) means True(x) >> (General_Knowledge ⊨ ~x) means False(x) >> ~True(x) & ~False(x) means x is not an element of General_Knowledge > > Eh? You made it sound like General_Knowledge was the system, rather than > a model, but there you have it as a model. > There is no model. It is all Rudolf Carnap Meaning Postulates that have every single nuance of 100% of their semantic meaning directly encoding in this formal language arranged in a knowledge ontology inheritance hierarchy. "cats" <are> "animals" is stipulated. How do we know that "cats" <are> "animals" ? It is an axiom of the set of atomic facts of the world. "animals" <are> "living things" is stipulated. How to we know that "cats" <are> "living things" "cats" <are> "animals" "animals" <are> "living things" Therefore "cats" <are> "living things" Ordinary syllogism. -- 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.
[toc] | [prev] | [next] | [standalone]
| From | Kaz Kylheku <643-408-1753@kylheku.com> |
|---|---|
| Date | 2025-11-26 21:42 +0000 |
| Message-ID | <20251126134210.19@kylheku.com> |
| In reply to | #641242 |
On 2025-11-26, olcott <polcott333@gmail.com> wrote: > "animals" <are> "living things" is stipulated. So a dead rabbit isn't an animal? Pure genius! -- TXR Programming Language: http://nongnu.org/txr Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal Mastodon: @Kazinator@mstdn.ca
[toc] | [prev] | [next] | [standalone]
| From | Kaz Kylheku <643-408-1753@kylheku.com> |
|---|---|
| Date | 2025-11-26 21:49 +0000 |
| Message-ID | <20251126134822.721@kylheku.com> |
| In reply to | #641244 |
On 2025-11-26, Kaz Kylheku <643-408-1753@kylheku.com> wrote: > On 2025-11-26, olcott <polcott333@gmail.com> wrote: >> "animals" <are> "living things" is stipulated. > > So a dead rabbit isn't an animal? How about Mickey Mouse? Living thing or not? Animal or not? -- TXR Programming Language: http://nongnu.org/txr Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal Mastodon: @Kazinator@mstdn.ca
[toc] | [prev] | [next] | [standalone]
Page 1 of 6 [1] 2 3 4 5 6 Next page →
Back to top | Article view | sci.math
csiph-web