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Groups > comp.theory > #136879
| From | Kaz Kylheku <046-301-5902@kylheku.com> |
|---|---|
| Newsgroups | comp.theory, sci.logic, sci.math, sci.lang |
| Subject | Re: A new category of thought |
| Date | 2025-11-29 22:44 +0000 |
| Organization | A noiseless patient Spider |
| Message-ID | <20251129141108.632@kylheku.com> (permalink) |
| References | (2 earlier) <10gfcpa$3ji8m$1@dont-email.me> <20251129121613.116@kylheku.com> <10gfmc1$3nf97$1@dont-email.me> <20251129132843.374@kylheku.com> <10gfqb6$3p2df$1@dont-email.me> |
Cross-posted to 4 groups.
On 2025-11-29, olcott <polcott333@gmail.com> wrote: > On 11/29/2025 3:39 PM, Kaz Kylheku wrote: >> On 2025-11-29, olcott <polcott333@gmail.com> wrote: >>> On 11/29/2025 2:23 PM, Kaz Kylheku wrote: >>>> On 2025-11-29, olcott <polcott333@gmail.com> wrote: >>>>> On 11/29/2025 11:53 AM, Kaz Kylheku wrote: >>>>>> On 2025-11-29, olcott <polcott333@gmail.com> wrote: >>>>>>> Any expression of language that is proven true entirely >>>>>>> on the basis of its meaning expressed in language is >>>>>>> a semantic tautology. >>>>>> >>>>>> A tautology is an expression of logic which is true for all >>>>>> combinations of the truth values of its variables and propositions, >>>>>> which is, of course, regardless of what they mean/represent. >>>>> >>>>> I did not say tautology. I said semantic tautology. >>>>> I am defining a new thing under the Sun. >>>> >>>> The existing tautology is already semantic. You have to know the >>>> semantics (the truth tables of the logical operators used in the >>>> formula, and the workings of quantifiers and whatnot) to be able to >>>> conclude whether a formula is a tautology. >>>> >>> >>> Try and show how Gödel incompleteness can be >>> specified in a language that can directly encode >>> self-reference and has its own provability operator >>> without hiding the actual semantics using Gödel numbers. >> >> The numbers are essential, because Gödel Incompleteness is >> about number theory. >> > > The generalization Gödel incompleteness applies to > every formal system that has arithmetic or better. And there you are, trying to take the numbers out of it. >> The Gödel Theorem involves a proof in which a certain number, >> the "Gödel number" that may be called G, is asserted to have >> a number-theoretical property. >> > > G := (F ⊬ G) // G says of itself that it is unprovable in F No, it doesn't; that is an outside interpretation of what it is saying. Gödel's sentence says that a certain number isn't a theorem-number. The interpretation that the number is the Gödel number of that very sentence is made externally to the sentence. Is there any part of your understanding that is accurate? >> An example of a number-theoretical property is "25 is a perfect >> square". Except we need it in more formal language. >> >> Gödel discovered that you can encode statements of number theory as >> integers, and manipulate them (e.g. do derivation) by arithmetic. >> > > That simply abstracts away the underlying semantics. > G is unprovable in F because G is semantically unsound, G is semantically sound, and can be adopted as an axiom. > We can't see that with Gödel numbers. A Gödel number can be decoded to recover the syntas of the formula. In the case of the Gödel sentence, we don't need to do that; we already know that the Gödel number decodes to that sentence. >> Then it became obvious that whether or not a formula is a theorem >> is a property of its Gödel number: a number-theoretical property. >> >> There are theorem-numbers and non-theorem-numbrers. >> >> The Gödel sentence says somethng like "The Gödel number >> calculated by the expression G is not a theorem-number." >> >> But G turns out to be the Gödel number of that very sentence >> itself. >>> >>>> Pick another word. Since only dimwitted crackpots like yourself will >>>> want to discuss anything using that word, keep the syllable count low >>>> and make sure there aren't too many off-centre vowels. >>> >>> Ad hominem the first choice of losers. >> >> I'm not making an argument; I'm suggesting a way of choosing >> an alternative word, since "tautology" is taken. >> >>>>> *Semantic tautology is stipulated to mean* >>>> >>>> Reject; call it something else. >>>> >>>>> Any expression of language that is proven true entirely >>>>> on the basis of its meaning expressed in language. >>>> >>>> You are gonna need to supply an example. >>> >>> The key is that a counter-example is categorically >>> impossible. >> >> So you are saying every expression in a certain language >> is proven true, so that its syntax admits no false sentences? > > It syntax admits anything that any human can > say in any language comprised of symbols. But that could be false. It is baffling by what you mean bhy "counter-example is categorically impossible"; at ths point it seems like a dodge from giving an example of sentence that is proven true entierly on the basis of its meaning expressed in language. >> What language is that, and what are examples? What happens >> when you try to make a false sentence? > > English, Second Order Predicate logic, C++... How does C++ express a sentence that is proven entirely true on the basis of its meaning expressed in a language; do you need templates or Boost? >> Is it possible to utter conjectures which later turn out false; >> and if so, then what happens? > > Conjectures are not elements of the body of knowledge. Some eventually are; but their syntax and meaning doesn't change. -- TXR Programming Language: http://nongnu.org/txr Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal Mastodon: @Kazinator@mstdn.ca
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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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