Formalizing Natural Language Semantics

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PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 11:38 pm
PeteOlcott wrote: Tue Mar 03, 2020 11:37 pm On what basis could you possibly justify the presumption that I am handling the counter-examples on a case by case basis?
1. On the basis of you saying so.
PeteOlcott wrote: Tue Mar 03, 2020 10:39 pm What I have accomplished is deriving the complete encoding (written in x86 machine language) of a halt decider that decides halting for the set of halting problem counter-examples as defined by the Peter Linz H_Hat.
2. If you had a universal solution you would've published the source code by now.
PeteOlcott wrote: Tue Mar 03, 2020 11:37 pm The Peter Linz H_Hat is a template that species an infinite set of Turing Machine descriptions.
Ohhh. You have an actual infinite set of Turing Machines? Show it to me!
You don't seem to understand these things very well do you?
If I were to write a computer program that could perform any arithmetic computation:
{-,+,*,/} a single program would function across an infinite set of pairs on input strings.

I could provide the program and you could see that it would do this.
You are also asking for the infinite set of strings input. That is ridiculous.
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 7:56 am
PeteOlcott wrote: Tue Mar 03, 2020 7:53 am (2) Since Tarski's whole Undefinability Theorem uses the Liar Paradox as it basis (1) Shows Tarski has no basis.
Sure. Quine has pointed out that analyticity is circular. Girard makes fun of Tarski through a lot of his work.
When quine pointed out his misconception of how analyticity is circular he did not consider this specification:
** Conceptual knowledge:
The set of all knowledge that can be completely expressed using language and verified as totally true entirely based on its meaning.
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 10:47 pm
PeteOlcott wrote: Tue Mar 03, 2020 10:39 pm a halt decider that decides halting for the set of halting problem counter-examples.
Pete, you are handling counter-examples on case-by-case basis. You are literally demonstrating that your solution is not universal!

How much more obvious than that does it get?
This comment was helpful for my work. On the basis of this comment I decided to proceed
with the most robust implementation that can be easily accomplished.

I have not solved the halting problem, I have refuted all of the conventional proofs that
show that the Halting Problem cannot be solved.
Skepdick
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Re: Formalizing Natural Language Semantics

Post by Skepdick »

PeteOlcott wrote: Wed Mar 04, 2020 4:16 pm The set of all knowledge that can be completely expressed using language and verified as totally true entirely based on its meaning.
You don't know what meaning is. You think meaning is semantics.

I am trying to tell you that grammar is more meaningful than semantics.
Skepdick
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Re: Formalizing Natural Language Semantics

Post by Skepdick »

PeteOlcott wrote: Wed Mar 04, 2020 4:10 pm You don't seem to understand these things very well do you?
If I were to write a computer program that could perform any arithmetic computation:
{-,+,*,/} a single program would function across an infinite set of pairs on input strings.

I could provide the program and you could see that it would do this.
You are also asking for the infinite set of strings input. That is ridiculous.
You have a very narrow view of this.

Arithmetic is a tiny, tiny sub-set of computation.

Any function you define can be seen as an operator. Don't think 2 + 2. Think plus(2,2)
Last edited by Skepdick on Wed Mar 04, 2020 4:35 pm, edited 1 time in total.
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 5:11 pm
PeteOlcott wrote: Tue Mar 03, 2020 4:11 pm To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.
Pete, you are a moron.

Proving that the Halting proofs are incorrect, is not the same thing as solving the halting problem.
PeteOlcott wrote: Tue Mar 03, 2020 4:11 pm I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.
That is not a universal solution to the halting problem. That is just an algorithm which provably halts.
You have re-invented Walther recursion.

In order to solve the halting problem I expect you to provide an algorithm, which can decide whether an arbitrary program, written in an arbitrary language will halt.

The word "arbitrary" means that you don't get to choose the program or the language in which it's written in.

It means that I get to choose the program/language. it also means that your algorithm MUST WORK for ALL programs written in ALL programming languages.
Proving that all of the conventional halting problem proofs are incorrect would be a very significant
accomplishment. On the basis of this proof others can come along and actually solve the halting
problem.

When building a very tall tower it is infeasible to do this on your own because there is too much work.
https://www.skyscrapercenter.com/buildi ... -khalifa/3

My refutation of Tarski and Gödel is more generic. I show how to reformulate the notion of a formal
system that has the same expressive power of existing formal systems yet in this new formal system
expression of language that would otherwise prove incompleteness are rejected as semantically
ill-formed truth-bearers.
Skepdick
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Re: Formalizing Natural Language Semantics

Post by Skepdick »

PeteOlcott wrote: Wed Mar 04, 2020 4:34 pm Proving that all of the conventional halting problem proofs are incorrect would be a very significant
accomplishment. On the basis of this proof others can come along and actually solve the halting
problem.
Then prove the simplest proof as being incorrect.

The one that's so simple that a 9 year old can understand it.
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 7:56 am
PeteOlcott wrote: Tue Mar 03, 2020 7:53 am (3) Since Tarski Undefinability is analogous to Gödel Incompleteness showing that Tarski is wrong proves that Gödel is also wrong.
ROFL. That's not how it works. Just because that one proof of incompleteness is wrong doesn't mean that incompleteness (in general) is wrong.
To provide the architecture of a formal system that is at least equally expressive as other formal system
yet always recognizes and rejects every expression of language that would otherwise show incompleteness
as a semantically ill-formed truth-bearer would prove that actual incompleteness does not actually exist.

People were mistaking expressions of language as proving incompleteness merely because their systems
lacked the basis to recognize that these expressions are not truth bearers.
Skepdick
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Re: Formalizing Natural Language Semantics

Post by Skepdick »

PeteOlcott wrote: Wed Mar 04, 2020 4:40 pm To provide the architecture of a formal system that is at least equally expressive as other formal system
yet always recognizes and rejects every expression of language that would otherwise show incompleteness
as a semantically ill-formed truth-bearer would prove that actual incompleteness does not actually exist.

People were mistaking expressions of language as proving incompleteness merely because their systems
lacked the basis to recognize that these expressions are not truth bearers.
Yeah, but Pete. You don't understand the context in which incompleteness is asserted.

Godel's argument was about "any reasonably powerful system which can say things about the numbers"
The numbers are infinite. And just from recognizing that the numbers are infinite, you should also recognize that an algorithm which simply mentions all of the numbers will never halt.

Completeness/Consistency are simply symptoms of infinities. All finite systems are complete. By brute-force.
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 7:56 am And if you quit being so damn dogmatic about it, you would've noticed by now that Turing's halting problem is not formulated either in Tarski or Gödel's frameworks. It stands on its own two feet. It's such a simple proof that as far as I am concerned it is conceptually prior (though, historically latter) to Gödel or Tarski.

To prove the Halting problem wrong is to produce an algorithm that solves the halting problem universally. We are still waiting.
I am not proving that the halting problem can be solved universally because that would require
more work than I have time for in the rest of my life. Instead I am proving that the conventional
proofs that it cannot be solved universally are incorrect.

I can show how the conventional halting problem proofs precisely frame their counter-examples
such that they become exactly the Liar Paradox. I just did that and could post the code that proves
what I said. I will include this code in the paper that I submit for publication. Academic journals
only want to publish unpublished work so I can't publish that here now.

I will also be able to provide fully operational code that shows the complete execution trace of
correctly deciding these sets of Liar-Paradox counter-examples.

The halt decider itself is written in standard "C" that compiles across platforms.
The Halting Problem counter-example is also written in standard "C" yet is compiled
using Microsoft Visual "C" because the generated code is much easier to understand.
Last edited by PeteOlcott on Wed Mar 04, 2020 8:04 pm, edited 1 time in total.
Skepdick
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Re: Formalizing Natural Language Semantics

Post by Skepdick »

PeteOlcott wrote: Wed Mar 04, 2020 5:02 pm I am not proving that the haling problem can be solved universally because that would require
more work than I have time for in the rest of my life. Instead I am proving that the conventional
proofs that it cannot be solved universally are incorrect.
Pete, that doesn't buy anybody anything!

We accept the halting problem as a fact of the universe. Irrespective of the proofs.

We understand empirically why the halting problem is true - it's an actual limit on what we can and can't do.

This Python function generates the set of ALL NATURAL NUMBERS.

Code: Select all

ℕ = lambda n=0: ℕ(n+1)
ℕ()
This function DOES NOT HALT. Surely you do not require a proof to understand why?
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Tue Mar 03, 2020 7:56 am
PeteOlcott wrote: Tue Mar 03, 2020 7:53 am As easy as 1,2,3 as long as you follow my detailed reasoning of 1,2,3.
I am not interested in your reasoning. I am interested in your universal algorithm. When it fails to do what you promise it will do, then you will know you are wrong.
>> Some expressions of language are stipulated to be true and some
>> relations between expressions of language are stipulated to be
>> truth preserving.

https://www.iep.utm.edu/quine-an/

This analytical / synthetic distinction overcomes Quine's objections:
**Conceptual knowledge:
The set of all knowledge that can be completely expressed using language and verified as
totally true entirely based on its meaning thus not requiring any sense data from the sense organs.

Any expression of language in this set can be proved to be true by tracing through the connected
set of semantic meanings that makes this expression of language true (as shown below).

If there is no connected set of meanings that makes an expression of language true, (and it is
not stipulated to be true) then this expression of language cannot be correctly evaluated as true.

From the stipulated definitions that [all dogs are mammals] and [all mammals are animals] we
can conclude that [all dogs are animals] by Aristotle's syllogism.

Copyright Pete Olcott 2019, 2020
Skepdick
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Re: Formalizing Natural Language Semantics

Post by Skepdick »

PeteOlcott wrote: Wed Mar 04, 2020 5:33 pm
Skepdick wrote: Tue Mar 03, 2020 7:56 am
PeteOlcott wrote: Tue Mar 03, 2020 7:53 am As easy as 1,2,3 as long as you follow my detailed reasoning of 1,2,3.
I am not interested in your reasoning. I am interested in your universal algorithm. When it fails to do what you promise it will do, then you will know you are wrong.
>> Some expressions of language are stipulated to be true and some
>> relations between expressions of language are stipulated to be
>> truth preserving.

https://www.iep.utm.edu/quine-an/

This analytical / synthetic distinction overcomes Quine's objections:
**Conceptual knowledge:
The set of all knowledge that can be completely expressed using language and verified as
totally true entirely based on its meaning thus not requiring any sense data from the sense organs.

Any expression of language in this set can be proved to be true by tracing through the connected
set of semantic meanings that makes this expression of language true (as shown below).

If there is no connected set of meanings that makes an expression of language true, (and it is
not stipulated to be true) then this expression of language cannot be correctly evaluated as true.

From the stipulated definitions that [all dogs are mammals] and [all mammals are animals] we
can conclude that [all dogs are animals] by Aristotle's syllogism.

Copyright Pete Olcott 2019, 2020
Pete, all you are concluding is that deduction deduces.

Sure! But deduction is for axiomatic systems. The universe isn't' one of those.

Formalisms are formalisms. Language is language. They serve a different purpose.

Language is inductive, not deductive.
Scott Mayers
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Re: Formalizing Natural Language Semantics

Post by Scott Mayers »

PeteOlcott wrote: Tue Mar 03, 2020 10:39 pm
Scott Mayers wrote: Tue Mar 03, 2020 9:01 pm
PeteOlcott wrote: Tue Mar 03, 2020 4:11 pm

To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.

I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.

http://liarparadox.org/Peter_Linz_HP%28 ... 319%29.pdf
We already recognize that you can solve any particular problem by careful exhaustion. What can't be done is to have a finite machine be able to FIND ALL the possible programs as 'haltable' finitely.
What I have accomplished is deriving the complete encoding (written in x86 machine language) of a halt decider that decides halting for the set of halting problem counter-examples as defined by the Peter Linz H_Hat.
My background is in machine languages. But I'm confused at what you assert such a program is doing up front. Turing presented a closed argument for ALL finite machines, which includes any machine and its languages built upon them. Prior to expecting me to look at such, I'd need to understand more about how you expect to find some/any alternative "halting decider" program that proves other "halting decider" programs used to discover whether you can list all programs that 'halt' has flaws without making those original ones work after all?

I think you might be misunderstanding the original arguments of incompleteness and the degree of their applications.

Another way of describing the problem is,

"Can you find an ideal single universal calculator that can solve all problems with complete satisfaction to solve all possible particular calculator-related problems there exists?"

Are you saying that you CAN, do not know, or cannot (but may have a disagreement about HOW the prior proofs have presented their case)?
PeteOlcott
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Re: Formalizing Natural Language Semantics

Post by PeteOlcott »

Skepdick wrote: Wed Mar 04, 2020 4:43 pm
PeteOlcott wrote: Wed Mar 04, 2020 4:40 pm To provide the architecture of a formal system that is at least equally expressive as other formal system
yet always recognizes and rejects every expression of language that would otherwise show incompleteness
as a semantically ill-formed truth-bearer would prove that actual incompleteness does not actually exist.

People were mistaking expressions of language as proving incompleteness merely because their systems
lacked the basis to recognize that these expressions are not truth bearers.
Yeah, but Pete. You don't understand the context in which incompleteness is asserted.

Godel's argument was about "any reasonably powerful system which can say things about the numbers"
The numbers are infinite. And just from recognizing that the numbers are infinite, you should also recognize that an algorithm which simply mentions all of the numbers will never halt.

Completeness/Consistency are simply symptoms of infinities. All finite systems are complete. By brute-force.
We define this as the body of analytic knowledge: (overcoming Quine's objections)
Analytic knowledge: The set of all knowledge that can be completely expressed using
language and verified as totally true entirely based on its meaning thus not requiring
any sense data from the sense organs.


We define a formal system on this basis:
Some expressions of language are stipulated to be true. ≅ AXIOMS
Some relations between expressions of language are stipulated to be truth preserving. ≅ rules-of-inference

Then we have unified sound deduction with formal proofs to theorem consequences.
When we restrict the notion of analytical truth to the above then only the conclusions
of sound deduction expressed as formal proofs to theorem consequences can be correctly
construed as true.

Wittgenstein applies this reasoning to refute Gödel's 1931 Incompleteness theorem:
http://www.liarparadox.org/Wittgenstein.pdf

Copyright 2020 Pete Olcott
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