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Groups > comp.theory > #136879

Re: A new category of thought

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.

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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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Thread

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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