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Groups > sci.math > #641406 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2025-11-29 10:32 -0600 |
| Last post | 2025-11-29 15:08 -0500 |
| Articles | 20 on this page of 100 — 11 participants |
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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 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 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
Page 4 of 5 — ← Prev page 1 2 3 [4] 5 Next page →
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-08 10:18 -0600 |
| Message-ID | <10h6tog$8c33$1@dont-email.me> |
| In reply to | #641730 |
On 12/8/2025 12:12 AM, Tristan Wibberley wrote:
> On 07/12/2025 10:42, Mikko wrote:
>> olcott kirjoitti 6.12.2025 klo 14.33:
>>> No one ever understands that my mathematical formal
>>> system includes the entire body of human general
>>> knowledge encoded in formalized English.
>
> Liar.
To be more precisely accurate I should have said I
have never seen any indication that anyone besides
me understands that any mathematical formalism could
contain the entire body of human general knowledge
encoded as formalized English.
>
>> Maybe because it is well understood that no formal system that can
>> be presented includes the entire body of human general knowledge.
>>
>
> Unless it also includes everything that is not of human general
> knowledge. Infinite monkeys and so forth.
>
That {cats are animals} is general knowledge that
Missy is a black cat with white spots owned
by a specific person at a specific location
is not general knowledge.
It seems that your objection that is not very
clearly worded is that you do not understand
whether or not and how a precise line of demarcation
can be drawn between general knowledge and
knowledge of a specific situation.
> Olcott already said it was a semantic tautology, after all. Which is a
> fancy way of saying that it's a system for universal semantic analysis
> so it contains all possible meaning associations including those that
> are of the body of human general knowledge.
>
Yes.
> Once he said it was a semantic tautology it was not possible to be
> surprising.
>
It seems to me that most people here try to avoid
understanding the meaning of the terms that I have
used and only care about rebuttal. That may have
changed recently when all of the trolls decided
to drop out in December.
> The difficult bit is as for a sculptor; to carve away those things that
> are /not/ wanted.
>
Merely a precise line of demarcation for
elements of the set of general knowledge
that can be expressed in language and those
that are not in this set.
Not Expressed in language: The actual first
hand sense stimulus from the sense organs.
General knowledge. (this is a first guess)
All the details of knowledge that is shared
across all of the various occupational categories
combined with common sense that has been encoded
in the Cyc project.
--
Copyright 2025 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning" computable.<br><br>
This required establishing a new foundation<br>
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| From | Kaz Kylheku <046-301-5902@kylheku.com> |
|---|---|
| Date | 2025-11-29 20:23 +0000 |
| Message-ID | <20251129121613.116@kylheku.com> |
| In reply to | #641415 |
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. 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. > *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. >> You would need to have tremendous stature in logic to >> be able to dictate a redefinition of a deeply entrenched, >> standard term. > > Or I could simply prove that I am correct on the Your intellectual track record shows that you couldn't prove correct your way out of a wet paper bag. > basis of the meaning of my words, thus anyone > disagreeing is merely proving that they are too > full of themselves. You are already wrong. The definition of word is neither correct nor incorrect. It's just accepted or not. A bad definition ahs some issue like circularty or inconsistency, but if there is no such problem, then the rest is just a matter of convention. I'm informing you that there is a convention already which assigns a meaning to "tautology". It is a semantic concept and therefore "semantic tautology" isn't readily distinguishable. -- TXR Programming Language: http://nongnu.org/txr Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal Mastodon: @Kazinator@mstdn.ca
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-29 14:51 -0600 |
| Message-ID | <10gfmc1$3nf97$1@dont-email.me> |
| In reply to | #641427 |
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. > 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. >> *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. >>> You would need to have tremendous stature in logic to >>> be able to dictate a redefinition of a deeply entrenched, >>> standard term. >> >> Or I could simply prove that I am correct on the > > Your intellectual track record shows that you couldn't prove correct > your way out of a wet paper bag. > Ad hominem the first choice of losers. >> basis of the meaning of my words, thus anyone >> disagreeing is merely proving that they are too >> full of themselves. > > You are already wrong. The definition of word is neither correct > nor incorrect. It's just accepted or not. A bad definition ahs > some issue like circularty or inconsistency, but if there is no > such problem, then the rest is just a matter of convention. > There you go, you are getting it now. circularity, inconsistency, and incoherence. > I'm informing you that there is a convention already which assigns > a meaning to "tautology". It is a semantic concept and therefore > "semantic tautology" isn't readily distinguishable. > -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-29 16:27 -0500 |
| Message-ID | <jzJWQ.9555$fEH6.6841@fx41.iad> |
| In reply to | #641430 |
On 11/29/25 3:51 PM, olcott 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. > Godel proved that such a system can't exist if it can represent the properties of the Natural Number. ASSUMING a provability operator exist has been shown to create an inconsistant system, if it supports the properties of the Natural numbers. (This is another of the proof you seem to want to assume isn't correct, but can't do anything about it) Just shows the error of assuming you can define a system with a given set of properties. > >> 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. > >>> *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. > >>>> You would need to have tremendous stature in logic to >>>> be able to dictate a redefinition of a deeply entrenched, >>>> standard term. >>> >>> Or I could simply prove that I am correct on the >> >> Your intellectual track record shows that you couldn't prove correct >> your way out of a wet paper bag. >> > > Ad hominem the first choice of losers. > >>> basis of the meaning of my words, thus anyone >>> disagreeing is merely proving that they are too >>> full of themselves. >> >> You are already wrong. The definition of word is neither correct >> nor incorrect. It's just accepted or not. A bad definition ahs >> some issue like circularty or inconsistency, but if there is no >> such problem, then the rest is just a matter of convention. >> > > There you go, you are getting it now. > circularity, inconsistency, and incoherence. > >> I'm informing you that there is a convention already which assigns >> a meaning to "tautology". It is a semantic concept and therefore >> "semantic tautology" isn't readily distinguishable. >> >
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-11-29 15:53 -0800 |
| Message-ID | <10gg10v$3r0gs$1@dont-email.me> |
| In reply to | #641432 |
On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
> Godel proved that such a system can't exist if it can represent the
> properties of the Natural Number.
I hope this can exist. Sorry for any typos with the n-ary tree, n=2
here. Can you notice any errors I missed? natural number in the tree
has two unique children. I can derive these children from any natural
number. I can get at a child's parent just from its mapped natural. It's
100% full circle.
0
/ \
/ \
1 2
/ \ / \
3 4 5 6
...........
The children of 1 are:
c[0] = 1 * 2 + 1 = 3
c[1] = c[0] + 1 = 4
Nice! Now, to map back
The parent of 3 is:
p = ceil(3 / 2) - 1 = 1
The parent of 4 is:
p = 4 / 2 - 1 = 1
The parent of 5 is:
p = ceil(5 / 2) - 1 = 2
The parent of 6 is:
p = 6 / 2 - 1 = 2
Notice I do not have to use ceil in the case of 2-ary when the natural
number in question is even? Premature optimization? ;^)
It works even with using ceil all the time:
Take the parent of 3 and 4:
p = ceil(3 / 2) - 1 = 1
p = ceil(4 / 2) - 1 = 1
Lets try a parent at zero with its 2-ary children of 1 and 2:
p = ceil(1 / 2) - 1 = 0
p = ceil(2 / 2) - 1 = 0
;^D
I need to adapt it for negative numbers. Think of the following 2-ary tree:
-1 -2
\ /
0
/ \
+1 +2
So, lets try it out... The children on the negative side of zero. Flip
things wrt +1 becomes -1:
c[0] = 0 * 2 - 1 = -1
c[1] = c[0] - 1 = -2
Well, that works! Let's get the parent of -2, and flip the sign on the
-1 to +1, should be zero: Also, lets flip ceil to floor:
p = floor(-2 / 2) + 1 = 0
Nice, lets try -1:
p = floor(-1 / 2) + 1 = 0
It works... Interesting to me.
Lets try -3, its parent should be -1:
p = floor(-3 / 2) + 1 = -1
Also, -4's parent should be -1:
p = floor(-4 / 2) + 1 = -1
Nice!
-5 and -6 should both have a parent of -2:
p = floor(-5 / 2) + 1 = -2
p = floor(-6 / 2) + 1 = -2
perfect.
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-29 19:17 -0500 |
| Message-ID | <P2MWQ.43771$zoq5.1168@fx42.iad> |
| In reply to | #641449 |
On 11/29/25 6:53 PM, Chris M. Thomasson wrote: > On 11/29/2025 1:27 PM, Richard Damon wrote: > [...] >> Godel proved that such a system can't exist if it can represent the >> properties of the Natural Number. So, where do you have a "provability operator" that will tell you if a given theory is in fact provable. That is what he showed can't exist. The problem is that there are an infinite number of possible proofs to see if any of them reach the desired statement. You can CHECK if a proof is validly proving the statement, but not determine if there exist such a proof, as the negative result requires infinite work. > > I hope this can exist. Sorry for any typos with the n-ary tree, n=2 > here. Can you notice any errors I missed? natural number in the tree > has two unique children. I can derive these children from any natural > number. I can get at a child's parent just from its mapped natural. It's > 100% full circle. > > 0 > / \ > / \ > 1 2 > / \ / \ > 3 4 5 6 > ........... > > The children of 1 are: > > c[0] = 1 * 2 + 1 = 3 > c[1] = c[0] + 1 = 4 > > > Nice! Now, to map back > > The parent of 3 is: > > p = ceil(3 / 2) - 1 = 1 > > > The parent of 4 is: > > p = 4 / 2 - 1 = 1 > > > The parent of 5 is: > > p = ceil(5 / 2) - 1 = 2 > > The parent of 6 is: > > p = 6 / 2 - 1 = 2 > > > Notice I do not have to use ceil in the case of 2-ary when the natural > number in question is even? Premature optimization? ;^) > > It works even with using ceil all the time: > > > Take the parent of 3 and 4: > > p = ceil(3 / 2) - 1 = 1 > p = ceil(4 / 2) - 1 = 1 > > > Lets try a parent at zero with its 2-ary children of 1 and 2: > > p = ceil(1 / 2) - 1 = 0 > p = ceil(2 / 2) - 1 = 0 > > > ;^D > > > I need to adapt it for negative numbers. Think of the following 2-ary tree: > > > -1 -2 > \ / > 0 > / \ > +1 +2 > > > So, lets try it out... The children on the negative side of zero. Flip > things wrt +1 becomes -1: > > c[0] = 0 * 2 - 1 = -1 > c[1] = c[0] - 1 = -2 > > Well, that works! Let's get the parent of -2, and flip the sign on the > -1 to +1, should be zero: Also, lets flip ceil to floor: > > p = floor(-2 / 2) + 1 = 0 > > Nice, lets try -1: > > p = floor(-1 / 2) + 1 = 0 > > > It works... Interesting to me. > > Lets try -3, its parent should be -1: > > p = floor(-3 / 2) + 1 = -1 > > Also, -4's parent should be -1: > > p = floor(-4 / 2) + 1 = -1 > > Nice! > > -5 and -6 should both have a parent of -2: > > > p = floor(-5 / 2) + 1 = -2 > p = floor(-6 / 2) + 1 = -2 > > perfect.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-11-29 16:35 -0800 |
| Message-ID | <10gg3g1$3rq3i$2@dont-email.me> |
| In reply to | #641450 |
On 11/29/2025 4:17 PM, Richard Damon wrote:
> On 11/29/25 6:53 PM, Chris M. Thomasson wrote:
>> On 11/29/2025 1:27 PM, Richard Damon wrote:
>> [...]
>>> Godel proved that such a system can't exist if it can represent the
>>> properties of the Natural Number.
>
> So, where do you have a "provability operator" that will tell you if a
> given theory is in fact provable.
Nope. That is not possible. Think of the integer 0. I can prove that it
has, wrt n-ary, n positive children, and n negative children. For
example, 2-ary, two (+) and two (-). Say n is a natural number:
-1 -2
\ /
\ /
(-0+) = the root of all? ;^)
/ \
/ \
+1 +2
But that is just for this n-ary case. I cannot just magically
extrapolate it our to some programming logic for some random program.
>
> That is what he showed can't exist.
>
> The problem is that there are an infinite number of possible proofs to
> see if any of them reach the desired statement.
>
> You can CHECK if a proof is validly proving the statement, but not
> determine if there exist such a proof, as the negative result requires
> infinite work.
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-29 20:10 -0500 |
| Message-ID | <QPMWQ.43776$zoq5.11775@fx42.iad> |
| In reply to | #641452 |
On 11/29/25 7:35 PM, Chris M. Thomasson wrote: > On 11/29/2025 4:17 PM, Richard Damon wrote: >> On 11/29/25 6:53 PM, Chris M. Thomasson wrote: >>> On 11/29/2025 1:27 PM, Richard Damon wrote: >>> [...] >>>> Godel proved that such a system can't exist if it can represent the >>>> properties of the Natural Number. >> >> So, where do you have a "provability operator" that will tell you if a >> given theory is in fact provable. > > Nope. That is not possible. Think of the integer 0. I can prove that it > has, wrt n-ary, n positive children, and n negative children. For > example, 2-ary, two (+) and two (-). Say n is a natural number: And that was the pre-condition Olcott made of his logic system, that it have a provability operator. Just like you can build a Halt Decider if you assume you have a correct halt decider (and ignore that it make the system inconsistant). > > -1 -2 > \ / > \ / > (-0+) = the root of all? ;^) > / \ > / \ > +1 +2 > > > But that is just for this n-ary case. I cannot just magically > extrapolate it our to some programming logic for some random program. > > > > > >> >> That is what he showed can't exist. >> >> The problem is that there are an infinite number of possible proofs to >> see if any of them reach the desired statement. >> >> You can CHECK if a proof is validly proving the statement, but not >> determine if there exist such a proof, as the negative result requires >> infinite work. > >
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-11-29 19:49 -0800 |
| Message-ID | <10ggerq$gvi$1@dont-email.me> |
| In reply to | #641457 |
On 11/29/2025 5:10 PM, Richard Damon wrote: > On 11/29/25 7:35 PM, Chris M. Thomasson wrote: >> On 11/29/2025 4:17 PM, Richard Damon wrote: >>> On 11/29/25 6:53 PM, Chris M. Thomasson wrote: >>>> On 11/29/2025 1:27 PM, Richard Damon wrote: >>>> [...] >>>>> Godel proved that such a system can't exist if it can represent the >>>>> properties of the Natural Number. >>> >>> So, where do you have a "provability operator" that will tell you if >>> a given theory is in fact provable. >> >> Nope. That is not possible. Think of the integer 0. I can prove that >> it has, wrt n-ary, n positive children, and n negative children. For >> example, 2-ary, two (+) and two (-). Say n is a natural number: > > And that was the pre-condition Olcott made of his logic system, that it > have a provability operator. > > Just like you can build a Halt Decider if you assume you have a correct > halt decider (and ignore that it make the system inconsistant). With 2-ary, two children per node, root node aside that has four children... Parent of nodes 1 and 2 is zero, root. Parent of nodes -1 and -2 is zero, root. (-2), (-1), (-0+), (+1), (+2) This seems rather consistent.? > >> >> -1 -2 >> \ / >> \ / >> (-0+) = the root of all? ;^) >> / \ >> / \ >> +1 +2 in 2-ary 0 has the following children (-1, -2, +1, +2), right? >> >> >> But that is just for this n-ary case. I cannot just magically >> extrapolate it our to some programming logic for some random program. >> >> >> >> >> >>> >>> That is what he showed can't exist. >>> >>> The problem is that there are an infinite number of possible proofs >>> to see if any of them reach the desired statement. >>> >>> You can CHECK if a proof is validly proving the statement, but not >>> determine if there exist such a proof, as the negative result >>> requires infinite work. >> >> >
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-11-29 19:50 -0800 |
| Message-ID | <10ggeu2$gvi$2@dont-email.me> |
| In reply to | #641457 |
On 11/29/2025 5:10 PM, Richard Damon wrote: > On 11/29/25 7:35 PM, Chris M. Thomasson wrote: >> On 11/29/2025 4:17 PM, Richard Damon wrote: >>> On 11/29/25 6:53 PM, Chris M. Thomasson wrote: >>>> On 11/29/2025 1:27 PM, Richard Damon wrote: >>>> [...] >>>>> Godel proved that such a system can't exist if it can represent the >>>>> properties of the Natural Number. >>> >>> So, where do you have a "provability operator" that will tell you if >>> a given theory is in fact provable. >> >> Nope. That is not possible. Think of the integer 0. I can prove that >> it has, wrt n-ary, n positive children, and n negative children. For >> example, 2-ary, two (+) and two (-). Say n is a natural number: > > And that was the pre-condition Olcott made of his logic system, that it > have a provability operator. [...] PO is a nut bar with extra nuts?
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| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2025-12-02 01:59 +0000 |
| Message-ID | <10glh69$1roie$3@dont-email.me> |
| In reply to | #641450 |
On 30/11/2025 00:17, Richard Damon wrote: > The problem is that there are an infinite number of possible proofs to > see if any of them reach the desired statement. > > You can CHECK if a proof is validly proving the statement, but not > determine if there exist such a proof, as the negative result requires > infinite work. The infinite number of possible proofs isn't the reason why because you are allowed induction in preference to enumeration. -- Tristan Wibberley The message body is Copyright (C) 2025 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-12-01 23:11 -0500 |
| Message-ID | <6GtXQ.51222$cfNb.26436@fx48.iad> |
| In reply to | #641556 |
On 12/1/25 8:59 PM, Tristan Wibberley wrote: > On 30/11/2025 00:17, Richard Damon wrote: >> The problem is that there are an infinite number of possible proofs to >> see if any of them reach the desired statement. >> >> You can CHECK if a proof is validly proving the statement, but not >> determine if there exist such a proof, as the negative result requires >> infinite work. > > The infinite number of possible proofs isn't the reason why because you > are allowed induction in preference to enumeration. > If there IS an induction property. If you can't find such an induction, you are stuck with having to confirm that the answer doesn't exist in the infinite set by testing each of them. Since Proofs are required to be finite, you can't search the infinite space in finite time unless you actually find the needed property (to perhaps use induction on). Godel's proof shows that unprovable but true statments exist in statement that support the basics of Natural Number mathematics.
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| From | Kaz Kylheku <046-301-5902@kylheku.com> |
|---|---|
| Date | 2025-11-29 21:39 +0000 |
| Message-ID | <20251129132843.374@kylheku.com> |
| In reply to | #641430 |
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 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. 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. 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? What language is that, and what are examples? What happens when you try to make a false sentence? Is it possible to utter conjectures which later turn out false; and if so, then what happens? >>>> You would need to have tremendous stature in logic to >>>> be able to dictate a redefinition of a deeply entrenched, >>>> standard term. >>> >>> Or I could simply prove that I am correct on the >> >> Your intellectual track record shows that you couldn't prove correct >> your way out of a wet paper bag. > > Ad hominem the first choice of losers. But anyway, your intellectual track record shows that you couldn't prove correct your way out of a wet paper bag. This is entirely relevant. You've never proven anything and never will. That contradicts your above claim that "I could simply prove ...". All evidence points to: no, you couldn't. >> You are already wrong. The definition of word is neither correct >> nor incorrect. It's just accepted or not. A bad definition ahs >> some issue like circularty or inconsistency, but if there is no >> such problem, then the rest is just a matter of convention. > > There you go, you are getting it now. > circularity, inconsistency, and incoherence. The existing definition of "tautology" doesn't have these issues. -- TXR Programming Language: http://nongnu.org/txr Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal Mastodon: @Kazinator@mstdn.ca
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-29 15:59 -0600 |
| Message-ID | <10gfqb6$3p2df$1@dont-email.me> |
| In reply to | #641435 |
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. > 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 > 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, We can't see that with Gödel numbers. > 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. > What language is that, and what are examples? What happens > when you try to make a false sentence? > English, Second Order Predicate logic, C++... > 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. >>>>> You would need to have tremendous stature in logic to >>>>> be able to dictate a redefinition of a deeply entrenched, >>>>> standard term. >>>> >>>> Or I could simply prove that I am correct on the >>> >>> Your intellectual track record shows that you couldn't prove correct >>> your way out of a wet paper bag. >> >> Ad hominem the first choice of losers. > > But anyway, your intellectual track record shows that you couldn't prove correct > your way out of a wet paper bag. > > This is entirely relevant. > > You've never proven anything and never will. > > That contradicts your above claim that "I could simply prove ...". > > All evidence points to: no, you couldn't. > >>> You are already wrong. The definition of word is neither correct >>> nor incorrect. It's just accepted or not. A bad definition ahs >>> some issue like circularty or inconsistency, but if there is no >>> such problem, then the rest is just a matter of convention. >> >> There you go, you are getting it now. >> circularity, inconsistency, and incoherence. > > The existing definition of "tautology" doesn't have these issues. > > It also is not rich enough to express anything that anyone can possibly say about anything. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Kaz Kylheku <046-301-5902@kylheku.com> |
|---|---|
| Date | 2025-11-29 22:44 +0000 |
| Message-ID | <20251129141108.632@kylheku.com> |
| In reply to | #641438 |
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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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-29 17:19 -0600 |
| Message-ID | <10gfv2d$3r0mk$1@dont-email.me> |
| In reply to | #641444 |
On 11/29/2025 4:44 PM, Kaz Kylheku wrote: > 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. That is EXACTLY what the above expression says. > Gödel's sentence says that a certain number isn't a theorem-number. > Which he says is merely his enormously convoluted way of saying this ...We are therefore confronted with a proposition which asserts its own unprovability. 15 … (Gödel 1931:40-41) Gödel, Kurt 1931. On Formally Undecidable Propositions of Principia Mathematica And Related Systems If you think that I am wrong then don't fucking guess show exactly what his sentence actually says without the ruse of Gödel numbers in a language has its own self-reference operator and provability operator. I say it says this: G := (F ⊬ G) // G says of itself that it is unprovable in F -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-29 19:21 -0500 |
| Message-ID | <V5MWQ.43772$zoq5.34811@fx42.iad> |
| In reply to | #641446 |
On 11/29/25 6:19 PM, olcott wrote: > On 11/29/2025 4:44 PM, Kaz Kylheku wrote: >> 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. > > That is EXACTLY what the above expression says. Right, but that isn't what Godel's G said. > >> Gödel's sentence says that a certain number isn't a theorem-number. >> > > Which he says is merely his enormously convoluted way of saying this Nope, because to convert Godel's statement to that requires "knowledge" that isn't in the system. > > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 … (Gödel 1931:40-41) Right, and that result was from logic in the META system, not the system. Your problem is you don't understand that basics of Formal Logic. > > Gödel, Kurt 1931. > On Formally Undecidable Propositions of Principia Mathematica And > Related Systems > > If you think that I am wrong then don't fucking guess > show exactly what his sentence actually says without > the ruse of Gödel numbers in a language has its own > self-reference operator and provability operator. Because the sentence isn't in the context of where you claim it to be in, You are just showing you don't understand the importance of Context > > I say it says this: > G := (F ⊬ G) // G says of itself that it is unprovable in F > Which just shows that you are a stupid liar that doesn't know what you are talking about, and don't care to learn how you are wrong, because you just don't care about the truth.
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| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2025-12-02 01:13 +0000 |
| Message-ID | <10glegf$1roie$1@dont-email.me> |
| In reply to | #641446 |
On 29/11/2025 23:19, olcott wrote:
> Gödel, Kurt 1931.
> On Formally Undecidable Propositions of Principia Mathematica And
> Related Systems
Do you have a reference to the original and also English translation of
his 1938 paper "On Formally Undecidable Propositions of Principia
Mathematica And Related Systems II"?
^^
His 1931 paper says he'll followup with a completed proof and
generalisation to more systems - so I think that's what we have to look
at to understand what people refer to as his first incompleteness proof
and theorem. I've been told (albeit by a chatbot) that the title and
year above is what I should look for.
> If you think that I am wrong then don't fucking guess
> show exactly what his sentence actually says without
> the ruse of Gödel numbers in a language has its own
> self-reference operator and provability operator.
You've gone off the deep end there.
> I say it says this:
> G := (F ⊬ G) // G says of itself that it is unprovable in F
It says that G is not a theorem of F, and perhaps it does so
epitheoretically because of the use of ":=" which often nominates a
substitution to apply to get an object of F, and that would /almost/
trivially make it true, albeit not for all possible F.
"[fact] in [a system]" conventionally can mean [fact] for all definition
extensions of [a system] when mathematicians are talking because they
add definitions when using the system and examine the consequences "/in/
the system". The prepositions are ambiguous across specialisms, clearly.
There are some more ambiguities so reflecting and responding usefully on
Olcott's expression is difficult and nondeterministic.
--
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.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-01 19:50 -0600 |
| Message-ID | <10glgm1$1st18$1@dont-email.me> |
| In reply to | #641553 |
On 12/1/2025 7:13 PM, Tristan Wibberley wrote: > On 29/11/2025 23:19, olcott wrote: > >> Gödel, Kurt 1931. >> On Formally Undecidable Propositions of Principia Mathematica And >> Related Systems > > Do you have a reference to the original and also English translation of > his 1938 paper "On Formally Undecidable Propositions of Principia > Mathematica And Related Systems II"? > ^^ > Gödel, Kurt 1931. On Formally Undecidable Propositions of Principia Mathematica And Related Systems https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf I never look at things in terms of their complex verbosity. As a software engineer with decades of experience I boil them down to their breast essence. > His 1931 paper says he'll followup with a completed proof and > generalisation to more systems - so I think that's what we have to look > at to understand what people refer to as his first incompleteness proof > and theorem. I've been told (albeit by a chatbot) that the title and > year above is what I should look for. > > >> If you think that I am wrong then don't fucking guess >> show exactly what his sentence actually says without >> the ruse of Gödel numbers in a language has its own >> self-reference operator and provability operator. > > You've gone off the deep end there. > Maybe with the swearing, these people have proven to be incorrigible, that is why I blocked half of them. > >> I say it says this: >> G := (F ⊬ G) // G says of itself that it is unprovable in F > > > It says that G is not a theorem of F, and perhaps it does so That is short-hand. > epitheoretically because of the use of ":=" which often nominates a > substitution to apply to get an object of F, and that would /almost/ > trivially make it true, albeit not for all possible F. > *YACC Syntax of Olcott Minimal Type Theory* https://philarchive.org/archive/PETMTT-4v2 I used the "defined as" operator to allow direct self-reference. > "[fact] in [a system]" conventionally can mean [fact] for all definition > extensions of [a system] when mathematicians are talking because they > add definitions when using the system and examine the consequences "/in/ > the system". The prepositions are ambiguous across specialisms, clearly. > I mean every fact that can be axiomatized in the the verbal model of the actual world. "cats" <are> "animals" stipulates relations between finite strings Implementing Gödel's "theory of simple types" in a type hierarchy of Rudolf Carnap Meaning Postulates. https://lawrencecpaulson.github.io/papers/Russells-mathematical-logic.pdf bottom of page 9 https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf > There are some more ambiguities so reflecting and responding usefully on > Olcott's expression is difficult and nondeterministic. > *YACC Syntax of Olcott Minimal Type Theory* https://philarchive.org/archive/PETMTT-4v2 Here I show Olcott's Minimal Type Theory and Prolog side-by-side with the Clocksin & Mellish showing the same infinite expansion. % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. In Olcott's Minimal Type Theory LP := ~True(LP) that expands to: ~True(~True(~True(~True(~True(LP))))) BEGIN:(Clocksin & Mellish 2003:254) Finally, a note about how Prolog matching sometimes differs from the unification used in Resolution. Most Prolog systems will allow you to satisfy goals like: equal(X, X). ?- equal(foo(Y), Y). that is, they will allow you to match a term against an uninstantiated subterm of itself. In this example, foo(Y) is matched against Y, which appears within it. As a result, Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of infinite structure. END:(Clocksin & Mellish 2003:254) % This sentence cannot be proven in F ?- G = not(provable(F, G)). G = not(provable(F, G)). ?- unify_with_occurs_check(G, not(provable(F, G))). false. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-12-01 13:02 +0200 |
| Message-ID | <10gjsku$18h21$1@dont-email.me> |
| In reply to | #641438 |
olcott kirjoitti 29.11.2025 klo 23.59: G := (F ⊬ G) // G says of itself that it is unprovable in F With a reasonable type system that is a type error: - the symbol ⊬ requires a sentence on the right side - the value of the ⊬ operation is a truth value - the symbol := requires the same type on both sides - thus G must be both a sentence and a truth value But G cannot be both. A sentence has a truth value but it isn't one. -- Mikko
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