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Re: What are Semantic Atoms ???

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peteolcott

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May 10, 2017, 12:18:53 PM5/10/17
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On 5/9/2017 2:01 AM, Franz Gnaedinger wrote:
> Pete Olcott goes into the next round, making ever the same claims, never
> advancing by one single step, never achieving anything real. Meanwhile
> a Swiss team of researchers developed a tool for better machine translation
> by considering not only the sentence to translate but also the further
> semantic context. Nothing like that ever comes from Pete Olcott. Always
> the biggestest claims but nothing real.
>

I have made good progress on transforming Minimal Type Theory into a computer language that will be able to automatically generate mathematical proofs based on a set of (finite string rewrite rules) axioms.

MINIMAL_TYPE_THEORY_ALPHABET
------------------------------------------------------
LOGICAL_AND "∧"
LOGICAL_OR "∨"
NEGATION "~"
FOR_ALL "∀"
THERE_EXISTS "∃"
LOGICAL_IMPLICATION "→"
LOGICAL_EQUIVALENCE "↔"
LEFT_PAREN "("
RIGHT_PAREN ")"
IDENTIFIER [A-Za-z_]+ | GREEK_LETTER

Symbols not used in FOPL
DOUBLE_QUOTE [\"]
ELEMENT_OF_TYPE "∈"
ASSIGNMENT "=" // Assign WFF to Propositional Variable
SYNTACTIC_CONSEQUENCE "⊢"
ELEMENTS_OF_TYPE "⊂"

Yesterday I adapted the lexical specification for MTT such that the lexical analyzer would ignore the UTF-8 byte order mark.

I am pretty sure that the design of the syntax of MTT is complete. I will double check this design and then encode it in the BNF required by YACC.

Last week I wrote all of the axioms defining FOPL logical symbols (besides the FOPL quantifiers). The axioms provide FOPL inference to MTT.

Last night I began working on defining the MTT axioms defining the FOPL quantifiers.

I already have a code generator that will be able to translate MTT expressions into their directed acyclic graph equivalent that I wrote in 2009.

Pete Olcott

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Jun 8, 2017, 9:39:02 AM6/8/17
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On 6/8/2017 1:12 AM, Franz Gnaedinger wrote:
>
>> Pete Olcott goes into the next round, making ever the same claims, never
>> advancing by one single step, never achieving anything real. Meanwhile
>> a Swiss team of researchers developed a tool for better machine translation
>> by considering not only the sentence to translate but also the further
>> semantic context. Nothing like that ever comes from Pete Olcott. Always
>> the biggestest claims but nothing real.
>
> Some four years ago, when Pete Olcott appeared for the first time in sci.lang,
> starting and maintaining seventeen parallel threads, piling big claim on bigger
> claim, telling us that he knows the absolute and complete and total truth,
> but never providing a useful insight, I adviced him to go for a real project.
> For example he might count word distances and thus maybe find out something
> on the structure of the human mind. He declined. Why should he go for such
> a project when he already knows the absolute and total and complete truth?
> Meanwhile a team of American researchers went for that project. They scanned
> 220 million websites, counted distances between words, and found telling
> vicinities. For example Peter professor and Jane painter are statistically
> relevant word pairs, revealing that men (Peter) are more often associated
> with the sciences (professor) and women (Jane) with art (painter). Now they
> can draw conclusions from that project while Pete Olcott goes on making
> big claims without offering a real insight.
>

I am aiming to provide the mathematical foundation for completing this project:
http://www.cyc.com/documentation/ontologists-handbook/

From a linguists point of view I am creating a formal system of semantic sub atomic compositionality.

Most linguists do not generally have the math background required for the formal semantics of natural language.

--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)


David Kleinecke

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Jun 8, 2017, 1:23:01 PM6/8/17
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Speaking as a linguist with mathematical training your various
attempts to create your dream of a theory remain inadequate both
linguistically and mathematically.

Pete Olcott

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Jun 8, 2017, 3:50:21 PM6/8/17
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This is concrete implementation of a key aspect of such a system:
http://liarparadox.org/Provability_with_Minimal_Type_Theory.pdf

That it is a key aspect of such a system is directly demonstrated in that this system closes the semantic gaps of the original (1931) Incompleteness Theorem showing the fundamental error of this proof.

I am currently in the process of transforming this design into a fully operational knowledge ontology that can concretely demonstrate semantic logical entailment on the basis of meaning postulate axioms.

Kaz Kylheku

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Jun 8, 2017, 4:23:07 PM6/8/17
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On 2017-06-08, Pete Olcott <Pe...@NoEmail.address> wrote:
> I am currently in the process of transforming this design into a fully
> operational knowledge ontology that can concretely demonstrate
> semantic logical entailment on the basis of meaning postulate axioms.

What you're stupidly missing is the fact that if you design a type
system to which some construct doesn't seem to conform, it could very
well be that your type system is lacking in power to give that construct
a type. It doesn't prove that the construct is ill-typed, let alone that
the construct is *absurd* due to being ill-typed.

You've just cherry-picked a stupid type system to suit your case;
an example of begging-the-question fallacy.

Pete Olcott

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Jun 8, 2017, 5:09:43 PM6/8/17
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Yes I just cherry picked the 1931 Incompleteness Theorem as the easiest of all formalisms to correctly refute:

G( ~∃Γ ⊂ PM (Γ ⊢ G) )  // Incompleteness Theorem as a named predicate

 

http://liarparadox.org/Provability_with_Minimal_Type_Theory.pdf

 

 


--

FS A) ≡ (Γ FS A)


Pete Olcott

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Jun 9, 2017, 9:04:21 AM6/9/17
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On 6/8/2017 4:59 PM, DKleinecke wrote:
> On Thursday, June 8, 2017 at 12:59:05 PM UTC-7, Pete Olcott wrote:

>> I am working on the YACC BNF syntax of Minimal Type Theory.
>> It will end up being a subset of "C" for functions and FOPL syntax (not semantics) that has been strongly typed using the proper classes of NBG axiomatic set theory.
>
> This I will have to see before I believe.
>

I have the first draft almost complete, I have one YACC shift-reduce conflict to resolve.
The FOPL portion is identical to FOPL, except that it is a strongly typed language, requiring that everything has its type explicitly specified.

Pete Olcott

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Jun 9, 2017, 9:15:07 AM6/9/17
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On 6/8/2017 5:00 PM, DKleinecke wrote:
> I could guess at your intentions - but why bother. Present
> a theory of MTT and we can comment.
>

http://www.cyc.com/documentation/ontologists-handbook/
It is the same sort of thing as CycL, except simpler and the key distinction is that the design of my system is based on sub atomic semantic compositionality where everything (semantics of all operators, rules of inference) besides machine memory addressing is explicitly specified as an axiom.

{Iteration:while, Selection:if-else, Sequence}
Types:
Character // UTF-32
String // of Characters
Index // __int64 subscript of String
Number // String of digits
Unit of composition: Function

David Kleinecke

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Jun 9, 2017, 11:15:52 AM6/9/17
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I hope you understand why that "explanation" is completely
inadequate.

Pete Olcott

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Jun 9, 2017, 11:32:59 AM6/9/17
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Certainly.  The LEX spec is completed the rough draft of YACC spec is nearly there.

Pete Olcott

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Jun 10, 2017, 2:32:56 PM6/10/17
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On 6/8/2017 3:23 PM, Kaz Kylheku wrote:
I am using sub atomic semantic compositionality (from my own formal linguistics theory) to specify a system of types such that these types are composed from the smallest possible constituent parts.

All other linguistic theories of formal semantics stop the decomposition at the atomic level, essentially one whole thought. I break it down further into the smallest possible micro elements of a complete thought.

Even the operators of my Minimal Type Theory (MTT) require their defining axioms to be explicitly specified otherwise these operators remain utterly meaningless.

Basically I formalize the entire set of all knowledge (mathematical and otherwise) simply as finite string transformation rules.

When I do this I discover key semantic gaps in the expressiveness of other formal systems.

One of these key gaps (Pathological Self Reference) was first mentioned in comp.theory On 9/5/2004 11:21 AM.

The directed acyclic graph of Minimal Type Theory finally explicitly formalizes the notion of PSR.
http://liarparadox.org/Provability_with_Minimal_Type_Theory.pdf

Peter Percival

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Jun 17, 2017, 9:43:24 AM6/17/17
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Pete Olcott wrote:
> [...]
> The FOPL portion is identical to FOPL, except that it is a strongly
> typed language, requiring that everything has its type explicitly
> specified.

It may be that what you want is a many-sorted first order theory. But
note that if S1 and S2 are sorts you may have, e.g.,

(forall x of sort S1)(exists y of sort S2)(...)

you may not have

(forall x of sort S1)(exists y subset of sort S2)(...)

because that is no longer first-order.
>


--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan

Pete Olcott

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Feb 23, 2018, 8:54:11 AM2/23/18
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On 2/23/2018 3:40 AM, Arnaud Fournet wrote:
> Le vendredi 23 février 2018 09:23:35 UTC+1, Franz Gnaedinger a écrit :
>>> Peter Olcott or Pete Olcott returned, and already starts multiplying his
>>> threads, instead of developing an idea in a single thread, so I revive
>>> this thread here, as he goes on reducing natural logic to mathematical
>>> logic, and driving life out of language.
>>
>> Peter Olcott is again multiplying his threads, decided to take over also
>> sci.lang in the name of his phantasm of the absolute and complete and total
>> truth, never saying anything understandable let alone useful about language,
>> providing ever more final and finaller and more ultamterer versions of his
>> alleged proofs that Goedel and Turing were wrong, not understanding their
>> work, claiming that the truth has always been his first priority, yet
>> dismissing some of the finest pieces of truth humankind achieved, the proven
>> theorems of Goedel and Turing, by mere word magic and lines that look as if
>> they were logical formulae but are not, which is why he never can finish
>> his papers, only shove around the bug.
>
> You're not the person most suited to write this,
> but I agree that Peter Olcott's outpours of delirium do not belong here.
> A.
>

What is Linguistics about if it is not about the notion of Truth within language? That none of you guys have enough math background to understand that I just refuted Tarski Undefinability is no indication what-so-ever that my posts pertaining to the same do not belong in sci.lang.

My Halting Problem proofs don't belong in a sci.lang forum and I only cross post some of them because there is a guy here that is also in the comp.theory forum.

To update the details of this post:

Semantic subatomic compositionality is the constituent parts of a semantic atom. A semantic atom is one whole relation/predicate from predicate logic.

Semantic atoms are connected to their constituent parts as the directed paths from nodes in a directed acyclic graph. Each node and each directed path of this Relation is a unit of subatomic semantic compositionality.

By forming these relations this way one can see for the first time how the constituent parts of a relation relate to each other in two dimensional space.

Higher Order Logic expressions are translated into directed acyclic graphs in strict left-to-right becomes top to bottom order. Identifiers are not duplicated.

The first reference to an identifier in a HOL expression is the only instance that is copied to the directed acyclic graph. All other references to this identifier have directed paths formed to this single reference.

By doing this we can see exactly how and why the Liar Paradox is semantically ungrounded as Kripke pointed out in his famous paper: [Outline of a Theory of Truth] Saul Kripke (1975)
http://web.dfc.unibo.it/paolo.leonardi/materiali/cs/Kripke.pdf

This is the key aspect of Minimal Type Theory that allows pathological self-reference(Olcott 2004) to be detected and rejected as semantically incorrect.

Prior to minimal type theory there were many expressions of language that were thought to be paradoxical rather than simply incorrect.

"This sentence is not true"
LP ≡ ~True(LP) // HOL with self-reference semantics

"This sentence is not provable"
G ≡ ~∃Γ Provable(Γ, G) // HOL with self-reference semantics

Tarski's undefinability theorem Wikipedia
"The undefinability theorem shows that this encoding cannot be done
for semantic concepts such as truth. It shows that no sufficiently
rich interpreted language can represent its own semantics."

The following link shows exactly how to define a Truth predicate in each formal or natural language, thus directly refuting Tarski by doing what he concluded was impossible.
http://liarparadox.org/index.php/2018/02/17/the-ultimate-foundation-of-a-priori-truth/

When we plug the Liar Paradox or the simplified Incompleteness Theorem into the above Truth formula we see that the David Hilbert style formalist syntactic logical inference chain (formal proof) never reaches either True or False.

Unlike historical misconceptions the 1931 GIT is not True and improvable, it is simply incorrect because it is neither True nor False.

Copyright 2016, 2017, 2018 Pete Olcott

--
*∀L ∈ Formal_Systems
∀X
True(L, X) ↔ ∃Γ ⊆ Axioms(L) Provable(Γ, X) *

casagi...@optonline.net

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Feb 23, 2018, 2:36:39 PM2/23/18
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Why don't you post so others can easily read ?!

You know, like the original post .

Pete Olcott

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Feb 23, 2018, 2:49:55 PM2/23/18
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On 2/23/2018 1:36 PM, casagi...@optonline.net wrote:
> Why don't you post so others can easily read ?!
>
> You know, like the original post .
>

This stuff has been evolving over time. Here are some key articles:

https://www.researchgate.net/publication/315367846_Minimal_Type_Theory_MTT

https://www.researchgate.net/publication/317953772_Provability_with_Minimal_Type_Theory

https://www.researchgate.net/publication/323268530_Defining_a_Decidability_Decider

Pete Olcott

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Feb 23, 2018, 3:17:23 PM2/23/18
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On 2/23/2018 1:32 PM, Peter T. Daniels wrote:
> On Friday, February 23, 2018 at 11:39:28 AM UTC-5, Pete Olcott wrote:
>> On 2/23/2018 9:12 AM, Peter T. Daniels wrote:
>>> On Friday, February 23, 2018 at 8:54:11 AM UTC-5, Pete Olcott wrote:
>
>>>> What is Linguistics about if it is not about the notion of Truth within language?
>>> Linguistics is about the structure of human language and its use by the
>>> individual in society; and about how it has changed over the centuries.
>>>
>>> Questions of Truth are not addressed by linguistics, but by philosophy.
>>
>> https://en.wikipedia.org/wiki/Truth-conditional_semantics
>> Actually all of formal semantics of natural language is anchored in the notion of Truth.
>
> Linguistics is not concerned with formal semantics, and formal semantics of
> natural language is impossible (as you demonstrate nearly daily).
>

Oxford Journal of Semantics https://academic.oup.com/jos/pages/About

Discourse Semantics with Information Structure 2018
https://academic.oup.com/jos/article/35/1/127/4808589?

The Logic of Intention Reports 2017
https://academic.oup.com/jos/article-abstract/34/4/587/4056489?

https://academic.oup.com/jos/article/29/2/145/1638740? 2012
https://academic.oup.com/jos/article-abstract/24/2/169/1666771? 2007

>>>> That none of you guys have enough math background to understand that I just refuted Tarski Undefinability is no indication what-so-ever that my posts pertaining to the same do not belong in sci.lang.
>>> It is such an indication; mathematics is not relevant to linguistics. There have
>>> been attempts over the years to apply mathematical models to the study of human
>>> language (beginning well before Chomsky), but they haven't produced illuminating
>>> results; even Chomsky had abandoned the approach (which apparently computer
>>> scientists still value) he devised in the mid 1950s.
>>
>> It is not really true that they have not produce illuminating results.
>> The actual case is that there are very few people that know enough semantics
>> and mathematics to fully appreciate the illuminating results that are produced.
>
> Whatever results it may have produced are not part of linguistics and not
> relevant to human language.

António Marques

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Feb 24, 2018, 12:16:16 AM2/24/18
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Pete Olcott <Pe...@NoEmail.address> wrote:
> My Halting Problem proofs don't belong in a sci.lang forum and I only
> cross post some of them because there is a guy here that is also in the comp.theory forum.

Come again? Where’s the... logic... in that?

Pete Olcott

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Feb 24, 2018, 12:42:33 AM2/24/18
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I want to always have three copies of every post archived.

António Marques

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Feb 24, 2018, 10:31:48 AM2/24/18
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Pete Olcott <Pe...@NoEmail.address> wrote:
> On 2/23/2018 11:16 PM, António Marques wrote:
>> Pete Olcott <Pe...@NoEmail.address> wrote:
>>> My Halting Problem proofs don't belong in a sci.lang forum and I only
>>> cross post some of them because there is a guy here that is also in the
>>> comp.theory forum.
>>
>> Come again? Where’s the... logic... in that?
>>
>
> I want to always have three copies of every post archived.

So you’re one of those who think USENET is their personal notepad?

Pete Olcott

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Feb 24, 2018, 11:00:29 AM2/24/18
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On 2/24/2018 9:31 AM, António Marques wrote:
> Pete Olcott <Pe...@NoEmail.address> wrote:
>> On 2/23/2018 11:16 PM, António Marques wrote:
>>> Pete Olcott <Pe...@NoEmail.address> wrote:
>>>> My Halting Problem proofs don't belong in a sci.lang forum and I only
>>>> cross post some of them because there is a guy here that is also in the
>>>> comp.theory forum.
>>>
>>> Come again? Where’s the... logic... in that?
>>>
>>
>> I want to always have three copies of every post archived.
>
> So you’re one of those who think USENET is their personal notepad?
>

As will be shown my work changes the foundation of mathematics
and computer science, thus must be well-documented.

The reason that I am doing this work is to establish the foundation
for the formalization of natural language.

The reason for doing that is to create a fully functional human
mind from non-living material (silicon and software).

Ben Bacarisse

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Feb 24, 2018, 4:16:43 PM2/24/18
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Pete Olcott <Pe...@NoEmail.address> writes:

> On 2/24/2018 9:31 AM, António Marques wrote:
<snip>
>> So you’re one of those who think USENET is their personal notepad?
>
> As will be shown my work changes the foundation of mathematics
> and computer science, thus must be well-documented.

What's extraordinary is that you can't see how this makes you look. Do
you have any friends or family whose opinion about social matters you
trust? If so, show them this post and take what they say about it
seriously. They don't have to know anything about mathematics, just
about how the world of academic ideas works. They might suggest you
seek help. I certainly would.

The foundation of mathematics gets changed by published papers, not by
doodles in some crank-infested corner of the internet. Even if your
ideas were new and sound, you would risk being mistaken for a crank
simply by not publishing in a proper journal.

--
Ben.

Helmut Richter

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Feb 25, 2018, 2:18:28 PM2/25/18
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[ Followup-To: poster ]

On Sat, 24 Feb 2018, Ben Bacarisse wrote:

> What's extraordinary is that you can't see how this makes you look. Do
> you have any friends or family whose opinion about social matters you
> trust? If so, show them this post and take what they say about it
> seriously. They don't have to know anything about mathematics, just
> about how the world of academic ideas works. They might suggest you
> seek help. I certainly would.
>
> The foundation of mathematics gets changed by published papers, not by
> doodles in some crank-infested corner of the internet. Even if your
> ideas were new and sound, you would risk being mistaken for a crank
> simply by not publishing in a proper journal.

Thank you for pointing out what Pete Olcott's problem is.

It is entirely irrelevant whether mathematical methods have ever had a
place in linguistics, and, if not, whether one can conclude that they will
never have. It is only relevant whether Pete Olcott can present results
that are mathematically sound, and only if so, whether he can explain in
which way they could be interesting for linguistics. As far as I have seen
in the past years, he has failed in both respects.

I urge everyone interested in one of the fields of the three usenet groups
never to respond in order to simply refute a contribution, but rather only
when something really interesting and relevant has been found in the
contribution one answers.

And the same hold for other the threads that have dominated sci.lang for
years.

--
Helmut Richter

Pete Olcott

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Feb 26, 2018, 1:11:21 AM2/26/18
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On 2/24/2018 3:16 PM, Ben Bacarisse wrote:
> Pete Olcott <Pe...@NoEmail.address> writes:
>
>> On 2/24/2018 9:31 AM, António Marques wrote:
> <snip>
>>> So you’re one of those who think USENET is their personal notepad?
>>
>> As will be shown my work changes the foundation of mathematics
>> and computer science, thus must be well-documented.
>
> The foundation of mathematics gets changed by published papers, not by
> doodles in some crank-infested corner of the internet. Even if your
> ideas were new and sound, you would risk being mistaken for a crank
> simply by not publishing in a proper journal.
>

I tried to get published three times and discovered that my words
could not be understood. I came here to progressively refine these
words until they can at least be understood.

Even though these groups may not have much credibility they
have proven to be the most effective process for incrementally
improving the quality of my words. David Kleinecke asked me
a series of questions that made one of my posts very much more effective.

These groups are the best in the world that I can get to actual peer
review. I am diligently striving to increase my level of professionalism.
I know that I will have to sound just like a PhD to get published. I
think that I have come a long way in the last five years towards this goal.

peteolcott

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Feb 26, 2018, 11:23:20 AM2/26/18
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On Sunday, February 25, 2018 at 1:18:28 PM UTC-6, Helmut Richter wrote:
> [ Followup-To: poster ]
>
> On Sat, 24 Feb 2018, Ben Bacarisse wrote:
>
> > What's extraordinary is that you can't see how this makes you look. Do
> > you have any friends or family whose opinion about social matters you
> > trust? If so, show them this post and take what they say about it
> > seriously. They don't have to know anything about mathematics, just
> > about how the world of academic ideas works. They might suggest you
> > seek help. I certainly would.
> >
> > The foundation of mathematics gets changed by published papers, not by
> > doodles in some crank-infested corner of the internet. Even if your
> > ideas were new and sound, you would risk being mistaken for a crank
> > simply by not publishing in a proper journal.
>
> Thank you for pointing out what Pete Olcott's problem is.
>
> It is entirely irrelevant whether mathematical methods have ever had a
> place in linguistics, and, if not, whether one can conclude that they will
> never have. It is only relevant whether Pete Olcott can present results
> that are mathematically sound, and only if so, whether he can explain in
> which way they could be interesting for linguistics. As far as I have seen
> in the past years, he has failed in both respects.
>

Here are mathematically sound results of applying formal logic to
specifying semantics in linguistics:

http://www.cyc.com/documentation/ontologists-handbook/writing-efficient-cycl/cycl-representation-choices/

> I urge everyone interested in one of the fields of the three usenet groups
> never to respond in order to simply refute a contribution, but rather only
> when something really interesting and relevant has been found in the
> contribution one answers.
>


All of my rebuttals have been of the form:
We know that you are wrong why don't you see this?
If they had been of the form this point here is mistaken for this
reason, I could correct the misunderstanding and show how I am
not mistaken.

Pete Olcott

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Feb 26, 2018, 12:31:14 PM2/26/18
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On 2/26/2018 2:11 AM, Arnaud Fournet wrote:
> I'm not that optimistic about your "progress".
> Basically, your semantic obsessions belong to linguistics just as much as marxist utopias belong to economics.
> I nevertheless agree that you're most probably less dangerous than marxists, unless you would try to have other people comply with your demented theories.
> You're a loonie, probably innocuous and harmless, and not at all a linguist.
> A.
>

I am having very much greater progress because my recent focus has
been on correcting the semantic gaps of formal mathematical languages.

The key progress that I recently made in formal languages can also
be directly applied to the formalization of natural languages because
the formalization of natural languages is anchored in truth conditional
semantics.

http://liarparadox.org/index.php/2018/02/17/the-ultimate-foundation-of-a-priori-truth/

By refuting Tarski's undefinability theorem and thus completing his
∀x True(x) ↔ φ(x) formula I have done what Tarski had "proved" to be
impossible and thus anchored the notion of Truth by specifying the
definition of a Truth predicate for each language of the collection
of all formal and natural languages.

One of the ways that I circumvented his findings was to define a
single formal language that can represent any arbitrary finite order
of logic from 0 to N. So even though some aspect of his language
hierarchy remains true the whole idea of separate languages being
required to specify this hierarchy has been refuted.

Minimal Type Theory can specify any finite order of logic from 0 to N
in a single very simple language that is based very slight augmentations
to the syntax of FOPL.

The details of my refutation of Tarski's undefinability theorem will be
provided later today on this link.

https://www.researchgate.net/publication/323268530_Defining_a_Decidability_Decider

The link currently only contains the definition of the Truth predicate that
Tarski "proved" does not exist.
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