On Monday, 19 December 2022 at 20:59:31 UTC+2, olcott wrote:
> Straighten up or be ignored henceforth.
You've promised to ignore me so many times and you lied every single time.

There's no reason to believe this time you are telling the truth.

On 12/18/2022 6:00 PM, Richard Damon wrote:
> On 12/18/22 10:35 AM, olcott wrote:
>> On 12/17/2022 11:33 AM, Richard Damon wrote:
>>> On 12/17/22 12:25 PM, olcott wrote:
>>>> On 12/16/2022 7:06 AM, Richard Damon wrote:
>>>>> On 12/16/22 12:28 AM, Skep Dick wrote:
>>>>>> On Friday, 16 December 2022 at 06:40:46 UTC+2, richar...@gmail.com
>>>>>> wrote:
>>>>>>> Nope, you are showing you don't understand the difference between
>>>>>>> Truth
>>>>>>> and Knowledge, and thus unqualified to talk about them.
>>>>>> Well, are you "qualified" to talk about them?
>>>>>>
>>>>>> You keep demonstrating (over and over) that if I gave you a bin
>>>>>> full of Truth and non-Truth all mixed up together you don't know
>>>>>> how to separate them.
>>>>>>
>>>>>> You don't know the (binary) classification rule for
>>>>>> recognizing/separating/sorting Truth from non-Truth.
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> But just asking someone to do that shows a lack of understanding of
>>>>> the nature of Truth.
>>>>>
>>>>> Not all Truth is Known, or even Knowable, therefore no one has the
>>>>> ability to completely sort every statement into the bins True and
>>>>> False (or not True).
>>>>
>>>> Every element of the body of analytic truth is only true on the
>>>> basis of
>>>> its semantic connections to other elements of the body of analytic
>>>> truth. Tracing through these connections is the proof of this truth.
>>>>
>>>> If these connections do not exist then an expression of language is
>>>> not a truth bearer.
>>>>
>>>
>>> Why? or maybe Why by this definition do you think it applies to
>>> Mathematics?
>>>
>>> You are defining that "Expressions of Language" are true or not by
>>> the meaning of their words.
>>>
>>> What in the meaning of the words"
>>>
>>
>> Expressions of language that cannot possibly be shown to be true on the
>> basis of their meaning are excluded form the body of analytic truth by
>> definition.
>
>
> The you must think that the Collatz Conjecture can not be an analytic
> statement, as it can't b4 shown true (or false) just on the meaning of
> the words.
>

I never said "meaning of words" please pay much more attention.
I never said "meaning of words" please pay much more attention.
I never said "meaning of words" please pay much more attention.
You replied to nine of my posts in four minutes.

The Collatz Conjecture is an expression of language with a currently
unknown truth value, thus the existence of a finite set of semantic
connections making it true or false is unknown. It cannot be currently
considered unprovable it can only be considered unproven.

> That means MOST of Mathematics is "outside" this Analytical space you
> are defining,

Not at all and you cannot provide correct reasoning to support this.

>>
>>>> Every positive even integer can be written as the sum of two primes.
>>>
>>> Determines if this statement is True or not?
>>>
>>> It seems that it hangs on the EXISTANCE or not of an even number that
>>> can't be expresses as the sum of two primes.
>>>
>>> To then say that it must be determinable by a FINITE sequence of
>>> steps, is a contradiction of definitions.
>>
>> This is the border case. It is obvious that it is not currently an
>> element of the body of analytic knowledge. It might be an element of the
>> body of analytic truth or not depending on exactly what "possibly be
>> shown to be true" means. I would say that because an infinite
>> enumeration cannot possibly occur that it may not be a truth bearer.
>>
>
> There is no "finite" connection limit on "Truth", only "Proof".
>

Any expression of language that is impossible to prove true or false is
by definition not a truth bearer.

Examples:
This sentence is not true.
This sentence cannot be proven
What time is it?

> (Please provide a reputable source if you disagree, otherwise it is just
> another of your ignorant claims)

The fact that the category of counter-examples is proven to be empty is
the proof that it is true.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/18/2022 6:01 PM, Richard Damon wrote:
> On 12/18/22 10:50 AM, olcott wrote:
>> On 12/17/2022 12:04 PM, Richard Damon wrote:
>>> On 12/17/22 12:35 PM, olcott wrote:
>>>> On 12/17/2022 10:08 AM, Richard Damon wrote:
>>>>> On 12/17/22 11:03 AM, olcott wrote:
>>>>>> On 12/16/2022 6:16 PM, Richard Damon wrote:
>>>>>>> On 12/16/22 11:29 AM, Skep Dick wrote:
>>>>>>>> On Friday, 16 December 2022 at 15:06:27 UTC+2,
>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>> On 12/16/22 12:28 AM, Skep Dick wrote:
>>>>>>>>>> On Friday, 16 December 2022 at 06:40:46 UTC+2,
>>>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>>>> Nope, you are showing you don't understand the difference
>>>>>>>>>>> between Truth
>>>>>>>>>>> and Knowledge, and thus unqualified to talk about them.
>>>>>>>>>> Well, are you "qualified" to talk about them?
>>>>>>>>>>
>>>>>>>>>> You keep demonstrating (over and over) that if I gave you a
>>>>>>>>>> bin full of Truth and non-Truth all mixed up together you
>>>>>>>>>> don't know how to separate them.
>>>>>>>>>>
>>>>>>>>>> You don't know the (binary) classification rule for
>>>>>>>>>> recognizing/separating/sorting Truth from non-Truth.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> But just asking someone to do that shows a lack of
>>>>>>>>> understanding of the
>>>>>>>>> nature of Truth.
>>>>>>>>>
>>>>>>>>> Not all Truth is Known, or even Knowable, therefore no one has the
>>>>>>>>> ability to completely sort every statement into the bins True
>>>>>>>>> and False
>>>>>>>>> (or not True).
>>>>>>>> This is so peculiar. If not all Truth is known or Knowable why
>>>>>>>> are you equating "not True" with False?
>>>>>>>>
>>>>>>>
>>>>>>> Because if a statement is a Truth Bearer, its only possibe values
>>>>>>> are True or False. There is no other option. PERIOD.
>>>>>>>
>>>>>>> We might not know the value of it, but it has one.
>>>>>>
>>>>>> Elements of the body of analytic truth are only true on the basis of
>>>>>> their semantic connections to other elements. When some of these
>>>>>> connections are unknown then these elements are in the body of
>>>>>> truth yet
>>>>>> missing from the body of knowledge.
>>>>>>
>>>>>
>>>>> And the problem is you are talking about fields that don't limit
>>>>> themselves to "analytic truth".
>>>>
>>>> It is common knowledge that math is a subset of analytic truth and your
>>>> ignorance of this basic fact is no rebuttal at all.
>>>>
>>>
>>> Maybe YOU think it is, but it isn't by your definition of Anayltical
>>> Truth.
>>>
>>> So your claim, with your definitions, is just WRONG.
>>>
>>> You inability to understand this just proves your ignorance and
>>> stupidity.
>>
>> It is stipulated that every expression of language that can be
>> determined to be true entirely based on its meaning without requiring
>> sense data form the sense organs is an analytic expression of language.
>>
>> Within the above stipulated definition all of mathematics and logic are
>> analytic expressions of language.
>
> So, how can the truth or falsehood of the Collatz conjecture be
> determined "entirely based on its meaning"?
>
> Seems you have stipulated yourself to be a liar.
>
>>
>> I see four rabbits on my lawn is an empirical expression of language
>> because it requires eyesight. 27 + 3 = 30 is analytic because it does
>> not require sense data from the sense organs to verify that it is true.
>>
>>
>
> So, is the fact that a proof exist based on senses or not?
>

Do you need to taste or smell an arithmetic expression as a part of
determining its value?

> If the mental process of searching the "space" of the system for a proof
> is considered analytic, then the Collatz conjecture might be provable
> false by finding a counter example, or it might be found true because

Yes.

> the infinte exhaustive search shoes that no such example exists.
>
> But an infinite search is NOT a valid proof, as a proof must have a
> finite number of steps.
>
> There is NOTHING in your definition that requires a finite number of
> steps to make a analytic expression true, only to be known.

Since I am only dealing with true/false/neither the Collatz conjecture
is outside the scope of this investigation. The Collatz conjecture is
provably true or false by a finite or infinite proof thus meeting my
requirements for True(x). Knowledge requires provably true or false by
finite proof.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/18/2022 6:02 PM, Richard Damon wrote:
> On 12/18/22 8:45 AM, Skep Dick wrote:
>> On Saturday, 17 December 2022 at 17:01:36 UTC+2, Mr Flibble wrote:
>>> Nope, your assertion is self referential/circular ergo it is a category
>>> error.
>> It is self-referential. Ergo the system is capable of reflection.
>>
>> https://en.wikipedia.org/wiki/Reflective_programming
>>
>> You call it an error. I call it a feature.
>>
>> The user is always right and I am the user.
>
> And the user shows that he is using an information free system so
> nothing he may have has any actual value.

Head is best ignored when he is only playing head games.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/18/2022 6:03 PM, Richard Damon wrote:
> On 12/18/22 10:20 AM, olcott wrote:
>> On 12/17/2022 10:54 AM, Richard Damon wrote:
>>> On 12/17/22 11:29 AM, olcott wrote:
>>>> On 12/16/2022 6:16 PM, Richard Damon wrote:
>>>>> On 12/16/22 2:24 PM, olcott wrote:
>>>>>> On 12/15/2022 10:39 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> Nope, because you are defining it in a way that you are requiring
>>>>>>> Mathematics to be based on it, but make it so that it can't be.
>>>>>>>
>>>>>>> You are showing your stupidity.
>>>>>>
>>>>>> Like I said you only know these things on the basis of
>>>>>> learned-by-rote
>>>>>> dogmatic rules thus haven't the slightest clue whether or not these
>>>>>> rules are consistent. When I point out that these rules are
>>>>>> inconsistent
>>>>>> you say that I am wrong because the rules do not say that they are
>>>>>> inconsistent.
>>>>>>
>>>>>
>>>>> And by that statement you are ADMITTING that you aren't using the a
>>>>> actual definitions of the field, and thus your statments don't have
>>>>> application to the field.
>>>>>
>>>>
>>>> You are merely asserting learned-by-rote that is anchored in ignorance
>>>> of the mandatory philosophical underpinnings.
>>>
>>> Nope, you are conflating your never-learned-because-of-ignorance for
>>> truth.
>>>
>>> You have proved this ignorance.
>>>
>>>>
>>>> I am established the foundation of correct reasoning that every logical
>>>> system must conform to otherwise it is incorrect.
>>>>
>>>
>>> And admitting you don't understand the existing systems, so LYING
>>> about your reasoning being applicable.
>>>
>>
>> Because my reasoning is categorical it applies to the infinite set of
>> all analytic truth. Every expression of language that cannot possibly be
>> proven or refuted is not a truth bearer. This include every logical
>> system that currently exists or all those that could be defined in the
>> future.
>>
>
> Nope, you reasoning is flawed because it is limited by your lack of
> understanding of the actual nature of logic, and things like the infinite.
>

Within the foundation of analytical truth an expression of language is
only true if it is either stipulated to be true or derived by applying
truth preserving operations to expressions of language having the
semantic property of Boolean true.

Every element of the body of analytic truth is only true on the basis of
its semantic connections to other elements of the body of analytic
truth. Tracing through these connections is the proof of this truth.

An expression of language that requires and infinite proof to show that
it is true or false is a truth bearer with an unknown truth value.

> That actually also shows that you CAN'T be the "God" you claim, as you
> become a contradiction. The Creator is greater than the cration,
>
>>>
>>>> To say that an expression of language is true and unprovable is the
>>>> same
>>>> sort of thing as saying that there is a person X that is both morbidly
>>>> obese and grossly underweight a contradiction in terms.
>>>>
>>>
>>> Nope, just shows how STUPID you are.
>>>
>>>> Every element of the body of analytic truth is only true on the
>>>> basis of
>>>> its semantic connections to other elements of the body of analytic
>>>> truth. Tracing through these connections is the proof of this truth.
>>>
>>> Confusing Truth with Knowledge.
>>>
>>
>> Every element of the body of analytic truth is only true on the basis of
>> its semantic connections to other elements of the body of analytic
>> truth. Tracing through these connections is the proof of this truth.
>
> And Truth can use an infinite number of connections, so might be
> unprovable.
>
>>
>>>>
>>>>> PERIOD.
>>>>>
>>>>> Any claims otherwize just proves you are a STUPID LIAR that doesn't
>>>>> understand how logic works.
>>>>>
>>>>
>>>> That you are utterly clueless about the philosophical foundations of
>>>> correct reasoning does not make me a liar.
>>>
>>> The fact that you claims things that you have no athority to claim does.
>>
>> The nature of truth itself is my full authority.
>
> Truth is what is True. You don't get to change the definition of it.
>
> In a field that accepts its version of "Empirical" (which in another
> sense is infinite modeled analytics), you don't get to say that it doesn't
>
>
>>
>>>>
>>>>> YOU ARE NOT GOD, and thus can't change the rules of the game.
>>>>>
>>>>
>>>> When the rules are shown to be incorrect then these rules can be
>>>> corrected.
>>>
>>> Nope, not unilaterally.
>>>
>>> You have just proved you are working outside the systems, so none of
>>> your work has any value, as you haven't shown that any of the things
>>> you are trying to talk about can even actually exist in your new
>>> logic system.
>>
>> There cannot possibly exist any counter-example to this statement:
>>
>> Every element of the body of analytic truth is only true on the basis of
>> its semantic connections to other elements of the body of analytic
>> truth. Tracing through these connections is the proof of this truth.
>
> But that only talks about "Analytic Truth", not all Truth is Analytic.
>
> Also, that definition allows for an infinte chain of connects to make
> something True, but such a chain is NOT a proof, as proofs are by
> definition, finite.
>
>>
>>>>
>>>>> If you want to claim you are, you will need to PROVE it.
>>>>
>>>
>>
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/18/2022 6:03 PM, Richard Damon wrote:
> On 12/18/22 10:23 AM, olcott wrote:
>> On 12/17/2022 10:55 AM, Richard Damon wrote:
>>> On 12/17/22 11:42 AM, olcott wrote:
>>>> On 12/16/2022 6:16 PM, Richard Damon wrote:
>>>>> On 12/16/22 10:34 AM, olcott wrote:
>>>>>> On 12/15/2022 8:27 PM, Richard Damon wrote:
>>>>>>> On 12/15/22 8:04 AM, Skep Dick wrote:
>>>>>>>> On Thursday, 15 December 2022 at 14:59:36 UTC+2,
>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>> Nope, because in mathematics with infinites you don't have
>>>>>>>>> those properties.
>>>>>>>>>
>>>>>>>>> That is one of the problems with infinities.
>>>>>>>>>
>>>>>>>>> You are assuming that all the properties of the finite numbers
>>>>>>>>> hold,
>>>>>>>>> which they don't.
>>>>>>>>
>>>>>>>> Where's the objective arbiter on such things?
>>>>>>>
>>>>>>> That they generate contradictions, and thus make the system
>>>>>>> worthless due to the power of the principle of explosion, since
>>>>>>> there can be no actual information or knowledge in such a system.
>>>>>>
>>>>>> The principle of explosion is incorrect because semantics are
>>>>>> ignored.
>>>>>
>>>>> So, you don't understand how logic works.
>>>>>
>>>>
>>>> It is because logic does not consistently know how correct reasoning
>>>> works. This correctly eliminates the principle of explosion:
>>>
>>> So, you are just proving you don't understand how logic works.
>>>
>>> You are proving your ignorance.
>>>
>>
>> The principle of explosion is self-evidently semantically incorrect.
>> Here is how to fix it: (A ∧ ¬A) := ε // empty string
>> thus (A ∧ ¬A) → B, B does not logically follow from the empty string.
>
> So, you don't understand the proof of the principle of explosion, as
> your example doesn't follow the form.
>
> You are just disproving a straw man
>

It is not that I do not understand the proof of the principle of
explosion. It is that I do understand that it derives nonsense.

There is no semantic connection from lemons to unicorns thus making it
the non-sequitur error even if learned-by-rote logicians disagree.

Logic is the woefully fallible human attempt at defining correct
reasoning and in some cases such as POE they missed the mark.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/20/22 11:08 AM, olcott wrote:
> On 12/18/2022 6:01 PM, Richard Damon wrote:
>
>> So, is the fact that a proof exist based on senses or not?
>>
>
> Do you need to taste or smell an arithmetic expression as a part of
> determining its value?
>

So, you don't answer the question.

Is the existance / non-existance of a proof determined by "senses" or not.

Analytically, non-existence can require the use of an INFINITE number of
operations.

Thus, the existance or non-existance of a proof is an actual FACT, but
might not be actually provable by a finite proof.

>> If the mental process of searching the "space" of the system for a
>> proof is considered analytic, then the Collatz conjecture might be
>> provable false by finding a counter example, or it might be found true
>> because
>
> Yes.

So you admit TRUTH can be based on an infinite number of steps, and thus
some TRUTH is not PROVABLE, because a proof must be finite.
>
>> the infinte exhaustive search shoes that no such example exists.
>>
>> But an infinite search is NOT a valid proof, as a proof must have a
>> finite number of steps.
>>
>> There is NOTHING in your definition that requires a finite number of
>> steps to make a analytic expression true, only to be known.
>
> Since I am only dealing with true/false/neither the Collatz conjecture
> is outside the scope of this investigation. The Collatz conjecture is
> provably true or false by a finite or infinite proof thus meeting my
> requirements for True(x). Knowledge requires provably true or false by
> finite proof.
>
>

The you logic can't handle the Natural Numbers by your own admission.

Your claim is that all Truth must be PROVABLE, not just determined by an
"infinite proof" (which is a oxymoron/contradictory statement).

This is EXACTLY the same distinction that comes in the halting problem,
the TRUTH of Halting might come from an infinite number of steps, but
the Decider must answer in a finite number, so some problems are not
correctly decidable.

On 12/20/22 10:43 AM, olcott wrote:
> On 12/18/2022 6:00 PM, Richard Damon wrote:
>> On 12/18/22 10:35 AM, olcott wrote:
>>> On 12/17/2022 11:33 AM, Richard Damon wrote:
>>>> On 12/17/22 12:25 PM, olcott wrote:
>>>>> On 12/16/2022 7:06 AM, Richard Damon wrote:
>>>>>> On 12/16/22 12:28 AM, Skep Dick wrote:
>>>>>>> On Friday, 16 December 2022 at 06:40:46 UTC+2,
>>>>>>> richar...@gmail.com wrote:
>>>>>>>> Nope, you are showing you don't understand the difference
>>>>>>>> between Truth
>>>>>>>> and Knowledge, and thus unqualified to talk about them.
>>>>>>> Well, are you "qualified" to talk about them?
>>>>>>>
>>>>>>> You keep demonstrating (over and over) that if I gave you a bin
>>>>>>> full of Truth and non-Truth all mixed up together you don't know
>>>>>>> how to separate them.
>>>>>>>
>>>>>>> You don't know the (binary) classification rule for
>>>>>>> recognizing/separating/sorting Truth from non-Truth.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>> But just asking someone to do that shows a lack of understanding
>>>>>> of the nature of Truth.
>>>>>>
>>>>>> Not all Truth is Known, or even Knowable, therefore no one has the
>>>>>> ability to completely sort every statement into the bins True and
>>>>>> False (or not True).
>>>>>
>>>>> Every element of the body of analytic truth is only true on the
>>>>> basis of
>>>>> its semantic connections to other elements of the body of analytic
>>>>> truth. Tracing through these connections is the proof of this truth.
>>>>>
>>>>> If these connections do not exist then an expression of language is
>>>>> not a truth bearer.
>>>>>
>>>>
>>>> Why? or maybe Why by this definition do you think it applies to
>>>> Mathematics?
>>>>
>>>> You are defining that "Expressions of Language" are true or not by
>>>> the meaning of their words.
>>>>
>>>> What in the meaning of the words"
>>>>
>>>
>>> Expressions of language that cannot possibly be shown to be true on the
>>> basis of their meaning are excluded form the body of analytic truth by
>>> definition.
>>
>>
>> The you must think that the Collatz Conjecture can not be an analytic
>> statement, as it can't b4 shown true (or false) just on the meaning of
>> the words.
>>
>
> I never said "meaning of words" please pay much more attention.
> I never said "meaning of words" please pay much more attention.
> I never said "meaning of words" please pay much more attention.

You said, and I qoute:
> Expressions of language that cannot possibly be shown to be true on the
> basis of their meaning are excluded form the body of analytic truth by
> definition.

What other meaning are you talking about then then meaning of the words.

> You replied to nine of my posts in four minutes.

Right, I hold off sending until I review the lot, to see if you make a
statement elsewhere applicable.

>
> The Collatz Conjecture is an expression of language with a currently
> unknown truth value, thus the existence of a finite set of semantic
> connections making it true or false is unknown. It cannot be currently
> considered unprovable it can only be considered unproven.
>

So, do you admit that it IS a Truth Bearer? Even if it might be true
that it can NEVER be proven?

>> That means MOST of Mathematics is "outside" this Analytical space you
>> are defining,
>
> Not at all and you cannot provide correct reasoning to support this.

IF the Collatz conjecture might not be an "analytic statement" then it
shows that your logic can't handle math, as mathematics considers it a
valid statement that is True or False.

If the Collatz conjecture IS accepted as an "analytic statement" even if
it might never be proven, then your assumption that all Truth is
provable is just shown to be FALSE.

Which is it then, are the undetermined statements of Mathematics outside
the ability of your logic system to process, and thus your logic system
incapable of handling current Mathematics, or is your statement that all
Analytic Statements are by necessity provable false?

>
>>>
>>>>> Every positive even integer can be written as the sum of two primes.
>>>>
>>>> Determines if this statement is True or not?
>>>>
>>>> It seems that it hangs on the EXISTANCE or not of an even number
>>>> that can't be expresses as the sum of two primes.
>>>>
>>>> To then say that it must be determinable by a FINITE sequence of
>>>> steps, is a contradiction of definitions.
>>>
>>> This is the border case. It is obvious that it is not currently an
>>> element of the body of analytic knowledge. It might be an element of the
>>> body of analytic truth or not depending on exactly what "possibly be
>>> shown to be true" means. I would say that because an infinite
>>> enumeration cannot possibly occur that it may not be a truth bearer.
>>>
>>
>> There is no "finite" connection limit on "Truth", only "Proof".
>>
>
> Any expression of language that is impossible to prove true or false is
> by definition not a truth bearer.

FALSE.

PROVE means a FINITE sequnence.
Some truth comes about from an INFINTE sequence of steps.

>
> Examples:
> This sentence is not true.
Right, a contracdiction.

> This sentence cannot be proven

Which MUST be true, as if it was false then it means it COULD be proven,
and thus must be True.

Note, Sentences of the form "x can be proven" or "x can not be proven"
are always Truth Bears as the proof either does or does not exist.

If z is not a truth bearer, then x can not be proven, as only True
statements can be proven, false statements as well non-truth beares can
not be proven.

> What time is it?

Not a true/false quesiton so not a "Truth Bearer". It does have a
"Corrct Answer" that depends on the context.

>> (Please provide a reputable source if you disagree, otherwise it is
>> just another of your ignorant claims)
>
> The fact that the category of counter-examples is proven to be empty is
> the proof that it is true.
>

So, not actual proof.

Fallacy of proof by example, which your repeated use shows that you fail
at your understanding if logic,

Showing that SOME statements meet your definition does not prove that
ALL statements meet your definition.

You just don't understand even the simple categorical logic rules.

On 12/20/22 11:25 AM, olcott wrote:

> Within the foundation of analytical truth an expression of language is
> only true if it is either stipulated to be true or derived by applying
> truth preserving operations to expressions of language having the
> semantic property of Boolean true.
>
> Every element of the body of analytic truth is only true on the basis of
> its semantic connections to other elements of the body of analytic
> truth. Tracing through these connections is the proof of this truth.
>
> An expression of language that requires and infinite proof to show that
> it is true or false is a truth bearer with an unknown truth value.

Which shows the differnce between Truth and Knowldge.

Those things that require an infinite proof to indicate it is true, are
things that are True but Unprovable/unknowable, as Proofs, by
definition, are FINITE sequence of steps.

If you want to allow infinite proofs in your system, you are using a
different language than everyone else, and need to change the term
"Unprovable" to "Unknowable" when reading otehr peoples work.

Incompleteness is essentially the assertion that there are some Truths
in the system that are not Provable (to you Knowable) in that system.

The problem with the term "Knowable" in this context is that generally
Knowability is allowed to leak between meta-systems and the system,
while provability is not.

If we know something from a meta-system with correspondance to the base
system, we consider that we KNOW it, but that doesn't show provablility
in the system.

So, allowing "Infinite Proofs" in your definitions reduces the
expresibility of your logic system.

On 12/20/22 11:38 AM, olcott wrote:
> On 12/18/2022 6:03 PM, Richard Damon wrote:
>> On 12/18/22 10:23 AM, olcott wrote:
>>> On 12/17/2022 10:55 AM, Richard Damon wrote:
>>>> On 12/17/22 11:42 AM, olcott wrote:
>>>>> On 12/16/2022 6:16 PM, Richard Damon wrote:
>>>>>> On 12/16/22 10:34 AM, olcott wrote:
>>>>>>> On 12/15/2022 8:27 PM, Richard Damon wrote:
>>>>>>>> On 12/15/22 8:04 AM, Skep Dick wrote:
>>>>>>>>> On Thursday, 15 December 2022 at 14:59:36 UTC+2,
>>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>>> Nope, because in mathematics with infinites you don't have
>>>>>>>>>> those properties.
>>>>>>>>>>
>>>>>>>>>> That is one of the problems with infinities.
>>>>>>>>>>
>>>>>>>>>> You are assuming that all the properties of the finite numbers
>>>>>>>>>> hold,
>>>>>>>>>> which they don't.
>>>>>>>>>
>>>>>>>>> Where's the objective arbiter on such things?
>>>>>>>>
>>>>>>>> That they generate contradictions, and thus make the system
>>>>>>>> worthless due to the power of the principle of explosion, since
>>>>>>>> there can be no actual information or knowledge in such a system.
>>>>>>>
>>>>>>> The principle of explosion is incorrect because semantics are
>>>>>>> ignored.
>>>>>>
>>>>>> So, you don't understand how logic works.
>>>>>>
>>>>>
>>>>> It is because logic does not consistently know how correct reasoning
>>>>> works. This correctly eliminates the principle of explosion:
>>>>
>>>> So, you are just proving you don't understand how logic works.
>>>>
>>>> You are proving your ignorance.
>>>>
>>>
>>> The principle of explosion is self-evidently semantically incorrect.
>>> Here is how to fix it: (A ∧ ¬A) := ε // empty string
>>> thus (A ∧ ¬A) → B, B does not logically follow from the empty string.
>>
>> So, you don't understand the proof of the principle of explosion, as
>> your example doesn't follow the form.
>>
>> You are just disproving a straw man
>>
>
>
> It is not that I do not understand the proof of the principle of
> explosion. It is that I do understand that it derives nonsense.
>
> There is no semantic connection from lemons to unicorns thus making it
> the non-sequitur error even if learned-by-rote logicians disagree.

So, you don;t understand how logic works.

>
> Logic is the woefully fallible human attempt at defining correct
> reasoning and in some cases such as POE they missed the mark.
>

And either you use the system as defined, or start your own whole
system, STARTING AT THE BEGFINNING.

Changing the initial definition, and then starting at the far end is
just an error, and shows you don't even understand your own rules (or
are just a hypocrit and don't follow them),

On 12/18/2022 6:03 PM, Richard Damon wrote:
> On 12/18/22 10:28 AM, olcott wrote:
>
>> It may be the case "there is no finite proof of Goldbach's conjecture"
>> is true and unknowable because the answer requires an infinite proof.
>>
>
> Which means you accept that there may exist a statement (which actually
> allows for statements) that is actually TRUE but which can not be
> actually PROVEN and thus is unknowable.
>
> This is because proofs, by definition, are finite.
>
> Thus, you admit that your logic system might be incomplete.
>

I never said that tracing through semantic connects had to be finite.
I only stipulated that when they do not exist then the expression of
language is not a truth bearer.

Every element of the body of analytic truth is only true on the basis of
its semantic connections to other elements of the body of analytic
truth. Tracing through these connections is the proof of this truth.

> In faxt, because of Godel's proof, which is similar, it is shown that it
> MUST be incomplete.
>
> How does it feel to admit that you whole work is proven wrong by your
> own words.

"This sentence is not provable." Is not provable because it is
self-contradictory and has a vacuous truth object.

This sentence is not true.
not true about what?
about being not true.
not true about being not true about what?

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/19/2022 12:20 PM, Richard Damon wrote:
> On 12/19/22 12:12 PM, olcott wrote:
>> On 12/19/2022 10:53 AM, Richard Damon wrote:
>>> On 12/19/22 10:33 AM, olcott wrote:
>>>
>>>> If every expression of language of analytical truth is only true on
>>>> the basis of its semantic connections to other elements of this set
>>>> then expressions of language that are true and unprovable cannot
>>>> possibly exist.
>>>>
>>>
>>> WHy do you say that?
>>>
>>> As I have said, Truth can exist from an INFINITE series of semantic
>>> connections, while proof requires a FINITE series of steps.
>>>
>>> All you are showing is that your mind doesn't comprehend the concepts
>>> of the infinite.
>>
>> Expressions of language are:
>> (1) True
>> (2) False
>> (3) Not truth bearers,
>> excluding all self contradictory expressions such as this:
>
> But actual self contradictory expressions just fall into your case (3),
> so aren't actually an excepting
>
>>
>> G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
>
> Which isn't G in F.
>

∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

There exists a G in F such that it is true that G is neither provable
nor refutable in F.

based on this foundational theorem (implied by Wittgenstein)
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

'True in Russell's system' means, as was said: proved in Russell's
system; and 'false in Russell's system' means: the opposite has been
proved in Russell's system. https://www.liarparadox.org/Wittgenstein.pdf

Otherwise we have unprovable (the not a truth bearer) or unproven
(unknown truth value).

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/20/22 11:44 AM, olcott wrote:
> On 12/18/2022 6:03 PM, Richard Damon wrote:
>> On 12/18/22 10:28 AM, olcott wrote:
>>
>>> It may be the case "there is no finite proof of Goldbach's conjecture"
>>> is true and unknowable because the answer requires an infinite proof.
>>>
>>
>> Which means you accept that there may exist a statement (which
>> actually allows for statements) that is actually TRUE but which can
>> not be actually PROVEN and thus is unknowable.
>>
>> This is because proofs, by definition, are finite.
>>
>> Thus, you admit that your logic system might be incomplete.
>>
>
> I never said that tracing through semantic connects had to be finite.
> I only stipulated that when they do not exist then the expression of
> language is not a truth bearer.

So you accept that there is a diffence between something True and
something Provable.

>
> Every element of the body of analytic truth is only true on the basis of
> its semantic connections to other elements of the body of analytic
> truth. Tracing through these connections is the proof of this truth.
>
>> In faxt, because of Godel's proof, which is similar, it is shown that
>> it MUST be incomplete.
>>
>> How does it feel to admit that you whole work is proven wrong by your
>> own words.
>
> "This sentence is not provable." Is not provable because it is
> self-contradictory and has a vacuous truth object.

But it is true, since no proof exists, something very demonstrable. The
only issue is that the "proof" of the statement can only be done with a
infintite search, or logic in a "meta-field" about the field.

This just shows you don't understand your own logic, or the definition
of what a PROOF is.

>
> This sentence is not true.
> not true about what?
> about being not true.
> not true about being not true about what?
>

On 12/20/22 11:52 AM, olcott wrote:
> On 12/19/2022 12:20 PM, Richard Damon wrote:
>> On 12/19/22 12:12 PM, olcott wrote:
>>> On 12/19/2022 10:53 AM, Richard Damon wrote:
>>>> On 12/19/22 10:33 AM, olcott wrote:
>>>>
>>>>> If every expression of language of analytical truth is only true on
>>>>> the basis of its semantic connections to other elements of this set
>>>>> then expressions of language that are true and unprovable cannot
>>>>> possibly exist.
>>>>>
>>>>
>>>> WHy do you say that?
>>>>
>>>> As I have said, Truth can exist from an INFINITE series of semantic
>>>> connections, while proof requires a FINITE series of steps.
>>>>
>>>> All you are showing is that your mind doesn't comprehend the
>>>> concepts of the infinite.
>>>
>>> Expressions of language are:
>>> (1) True
>>> (2) False
>>> (3) Not truth bearers,
>>> excluding all self contradictory expressions such as this:
>>
>> But actual self contradictory expressions just fall into your case
>> (3), so aren't actually an excepting
>>
>>>
>>> G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
>>
>> Which isn't G in F.
>>
>
> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

That isn't G in F.

G is actual a statement like

There does not exist a Natural Number 'n' that satisfies the property R
defined via a specfic primatitve recursive relationship (defined in the
proof).

The key point is that in the meta, it is shown that a number n that
satisfies the property R encodes a proof of the statement G in F.

>
> There exists a G in F such that it is true that G is neither provable
> nor refutable in F.
>
> based on this foundational theorem (implied by Wittgenstein)
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>
> 'True in Russell's system' means, as was said: proved in Russell's
> system; and 'false in Russell's system' means: the opposite has been
> proved in Russell's system. https://www.liarparadox.org/Wittgenstein.pdf

Which since Russel's system doesn't use that definition of Truth, it is
an inccorect statement, and the following is all unsound logic.

That was just Wittgenstein making incorrect assumptions because of his
own bias in logic.

Which you repeat because you haven't learn from history, because you are
just ignorant.

>
> Otherwise we have unprovable (the not a truth bearer) or unproven
> (unknown truth value).
>

Which since you are using the wrong definition of G, apparently because
of just using a bad knowledge of the cliff note versions of the
description of Godel's theorem, your proof doesn't actual mean anything.

On 12/20/2022 10:41 AM, Richard Damon wrote:
> On 12/20/22 11:08 AM, olcott wrote:
>> On 12/18/2022 6:01 PM, Richard Damon wrote:
>>
>>> So, is the fact that a proof exist based on senses or not?
>>>
>>
>> Do you need to taste or smell an arithmetic expression as a part of
>> determining its value?
>>
>
> So, you don't answer the question.
>
> Is the existance / non-existance of a proof determined by "senses" or not.
>

The answer to the question was answered by my question.
No it is not. Very obviously not.

> Analytically, non-existence can require the use of an INFINITE number of
> operations.
>
> Thus, the existance or non-existance of a proof is an actual FACT, but
> might not be actually provable by a finite proof.

OK so some things are unknown.

>>> If the mental process of searching the "space" of the system for a
>>> proof is considered analytic, then the Collatz conjecture might be
>>> provable false by finding a counter example, or it might be found
>>> true because
>>
>> Yes.
>
> So you admit TRUTH can be based on an infinite number of steps, and thus
> some TRUTH is not PROVABLE, because a proof must be finite.

If an expression of language is true there must be a complete set of
semantic connections making it true otherwise it is untrue.

>>
>>> the infinte exhaustive search shoes that no such example exists.
>>>
>>> But an infinite search is NOT a valid proof, as a proof must have a
>>> finite number of steps.
>>>
>>> There is NOTHING in your definition that requires a finite number of
>>> steps to make a analytic expression true, only to be known.
>>
>> Since I am only dealing with true/false/neither the Collatz conjecture
>> is outside the scope of this investigation. The Collatz conjecture is
>> provably true or false by a finite or infinite proof thus meeting my
>> requirements for True(x). Knowledge requires provably true or false by
>> finite proof.
>>
>>
>
> The you logic can't handle the Natural Numbers by your own admission.
>

No human logic can possibly complete an infinite set of operations in
finite time.

> Your claim is that all Truth must be PROVABLE, not just determined by an
> "infinite proof" (which is a oxymoron/contradictory statement).
>

If an expression of language is true there must be a complete set of
semantic connections making it true otherwise it is untrue.

> This is EXACTLY the same distinction that comes in the halting problem,
> the TRUTH of Halting might come from an infinite number of steps, but
> the Decider must answer in a finite number, so some problems are not
> correctly decidable.
--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/20/2022 10:41 AM, Richard Damon wrote:
> On 12/20/22 10:43 AM, olcott wrote:
>> On 12/18/2022 6:00 PM, Richard Damon wrote:
>>> On 12/18/22 10:35 AM, olcott wrote:
>>>> On 12/17/2022 11:33 AM, Richard Damon wrote:
>>>>> On 12/17/22 12:25 PM, olcott wrote:
>>>>>> On 12/16/2022 7:06 AM, Richard Damon wrote:
>>>>>>> On 12/16/22 12:28 AM, Skep Dick wrote:
>>>>>>>> On Friday, 16 December 2022 at 06:40:46 UTC+2,
>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>> Nope, you are showing you don't understand the difference
>>>>>>>>> between Truth
>>>>>>>>> and Knowledge, and thus unqualified to talk about them.
>>>>>>>> Well, are you "qualified" to talk about them?
>>>>>>>>
>>>>>>>> You keep demonstrating (over and over) that if I gave you a bin
>>>>>>>> full of Truth and non-Truth all mixed up together you don't know
>>>>>>>> how to separate them.
>>>>>>>>
>>>>>>>> You don't know the (binary) classification rule for
>>>>>>>> recognizing/separating/sorting Truth from non-Truth.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> But just asking someone to do that shows a lack of understanding
>>>>>>> of the nature of Truth.
>>>>>>>
>>>>>>> Not all Truth is Known, or even Knowable, therefore no one has
>>>>>>> the ability to completely sort every statement into the bins True
>>>>>>> and False (or not True).
>>>>>>
>>>>>> Every element of the body of analytic truth is only true on the
>>>>>> basis of
>>>>>> its semantic connections to other elements of the body of analytic
>>>>>> truth. Tracing through these connections is the proof of this truth.
>>>>>>
>>>>>> If these connections do not exist then an expression of language
>>>>>> is not a truth bearer.
>>>>>>
>>>>>
>>>>> Why? or maybe Why by this definition do you think it applies to
>>>>> Mathematics?
>>>>>
>>>>> You are defining that "Expressions of Language" are true or not by
>>>>> the meaning of their words.
>>>>>
>>>>> What in the meaning of the words"
>>>>>
>>>>
>>>> Expressions of language that cannot possibly be shown to be true on the
>>>> basis of their meaning are excluded form the body of analytic truth by
>>>> definition.
>>>
>>>
>>> The you must think that the Collatz Conjecture can not be an analytic
>>> statement, as it can't b4 shown true (or false) just on the meaning
>>> of the words.
>>>
>>
>> I never said "meaning of words" please pay much more attention.
>> I never said "meaning of words" please pay much more attention.
>> I never said "meaning of words" please pay much more attention.
>
> You said, and I qoute:
>> Expressions of language that cannot possibly be shown to be true on the
>> basis of their meaning are excluded form the body of analytic truth by
>> definition.
>
> What other meaning are you talking about then then meaning of the words.
>

You never heard of formal languages that do not use words?
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

>> You replied to nine of my posts in four minutes.
>
> Right, I hold off sending until I review the lot, to see if you make a
> statement elsewhere applicable.
>
>>
>> The Collatz Conjecture is an expression of language with a currently
>> unknown truth value, thus the existence of a finite set of semantic
>> connections making it true or false is unknown. It cannot be currently
>> considered unprovable it can only be considered unproven.
>>
>
> So, do you admit that it IS a Truth Bearer? Even if it might be true
> that it can NEVER be proven?
>

If an expression of language is true there must be a complete set of
semantic connections making it true otherwise it is untrue.

>>> That means MOST of Mathematics is "outside" this Analytical space you
>>> are defining,
>>
>> Not at all and you cannot provide correct reasoning to support this.
>
> IF the Collatz conjecture might not be an "analytic statement" then it
> shows that your logic can't handle math, as mathematics considers it a
> valid statement that is True or False.
>
> If the Collatz conjecture IS accepted as an "analytic statement" even if
> it might never be proven, then your assumption that all Truth is
> provable is just shown to be FALSE.
>

If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

> Which is it then, are the undetermined statements of Mathematics outside
> the ability of your logic system to process, and thus your logic system
> incapable of handling current Mathematics, or is your statement that all
> Analytic Statements are by necessity provable false?
>
>>
>>>>
>>>>>> Every positive even integer can be written as the sum of two primes.
>>>>>
>>>>> Determines if this statement is True or not?
>>>>>
>>>>> It seems that it hangs on the EXISTANCE or not of an even number
>>>>> that can't be expresses as the sum of two primes.
>>>>>
>>>>> To then say that it must be determinable by a FINITE sequence of
>>>>> steps, is a contradiction of definitions.
>>>>
>>>> This is the border case. It is obvious that it is not currently an
>>>> element of the body of analytic knowledge. It might be an element of
>>>> the
>>>> body of analytic truth or not depending on exactly what "possibly be
>>>> shown to be true" means. I would say that because an infinite
>>>> enumeration cannot possibly occur that it may not be a truth bearer.
>>>>
>>>
>>> There is no "finite" connection limit on "Truth", only "Proof".
>>>
>>
>> Any expression of language that is impossible to prove true or false
>> is by definition not a truth bearer.
>
> FALSE.
>
> PROVE means a FINITE sequnence.
> Some truth comes about from an INFINTE sequence of steps.
>

If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

>>
>> Examples:
>> This sentence is not true.
> Right, a contracdiction.
>
>> This sentence cannot be proven
>
> Which MUST be true, as if it was false then it means it COULD be proven,
> and thus must be True.
>
> Note, Sentences of the form "x can be proven" or "x can not be proven"
> are always Truth Bears as the proof either does or does not exist.
>

It is {truth bearer} not and animal with a furry body.

> If z is not a truth bearer, then x can not be proven, as only True
> statements can be proven, false statements as well non-truth beares can
> not be proven.
>
>> What time is it?
>
> Not a true/false quesiton so not a "Truth Bearer". It does have a
> "Corrct Answer" that depends on the context.
>

You got that correctly !

>
>
>>> (Please provide a reputable source if you disagree, otherwise it is
>>> just another of your ignorant claims)
>>
>> The fact that the category of counter-examples is proven to be empty
>> is the proof that it is true.
>>
>
> So, not actual proof.

Of every proof that can possibly exist there is no proof that correctly
concludes that a baby kitten is a type of ten story office building.

Of every proof that can possibly exist there is no counter-example to
this because it is true by definition:

If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

On 12/20/2022 10:41 AM, Richard Damon wrote:
> On 12/20/22 11:25 AM, olcott wrote:
>
>> Within the foundation of analytical truth an expression of language is
>> only true if it is either stipulated to be true or derived by applying
>> truth preserving operations to expressions of language having the
>> semantic property of Boolean true.
>>
>> Every element of the body of analytic truth is only true on the basis of
>> its semantic connections to other elements of the body of analytic
>> truth. Tracing through these connections is the proof of this truth.
>>
>> An expression of language that requires and infinite proof to show
>> that it is true or false is a truth bearer with an unknown truth value.
>
> Which shows the differnce between Truth and Knowldge.
>
> Those things that require an infinite proof to indicate it is true, are
> things that are True but Unprovable/unknowable, as Proofs, by
> definition, are FINITE sequence of steps.
>
> If you want to allow infinite proofs in your system, you are using a
> different language than everyone else, and need to change the term
> "Unprovable" to "Unknowable" when reading otehr peoples work.
>

If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

> Incompleteness is essentially the assertion that there are some Truths
> in the system that are not Provable (to you Knowable) in that system.
>

Therefore specifying this foundational theorem
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

> The problem with the term "Knowable" in this context is that generally
> Knowability is allowed to leak between meta-systems and the system,
> while provability is not.
>

I just addressed that. Based on the above foundational theorem:
∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

> If we know something from a meta-system with correspondance to the base
> system, we consider that we KNOW it, but that doesn't show provablility
> in the system.
>
> So, allowing "Infinite Proofs" in your definitions reduces the
> expresibility of your logic system.

If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/20/2022 10:43 AM, Richard Damon wrote:
> On 12/20/22 11:38 AM, olcott wrote:
>> On 12/18/2022 6:03 PM, Richard Damon wrote:
>>> On 12/18/22 10:23 AM, olcott wrote:
>>>> On 12/17/2022 10:55 AM, Richard Damon wrote:
>>>>> On 12/17/22 11:42 AM, olcott wrote:
>>>>>> On 12/16/2022 6:16 PM, Richard Damon wrote:
>>>>>>> On 12/16/22 10:34 AM, olcott wrote:
>>>>>>>> On 12/15/2022 8:27 PM, Richard Damon wrote:
>>>>>>>>> On 12/15/22 8:04 AM, Skep Dick wrote:
>>>>>>>>>> On Thursday, 15 December 2022 at 14:59:36 UTC+2,
>>>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>>>> Nope, because in mathematics with infinites you don't have
>>>>>>>>>>> those properties.
>>>>>>>>>>>
>>>>>>>>>>> That is one of the problems with infinities.
>>>>>>>>>>>
>>>>>>>>>>> You are assuming that all the properties of the finite
>>>>>>>>>>> numbers hold,
>>>>>>>>>>> which they don't.
>>>>>>>>>>
>>>>>>>>>> Where's the objective arbiter on such things?
>>>>>>>>>
>>>>>>>>> That they generate contradictions, and thus make the system
>>>>>>>>> worthless due to the power of the principle of explosion, since
>>>>>>>>> there can be no actual information or knowledge in such a system.
>>>>>>>>
>>>>>>>> The principle of explosion is incorrect because semantics are
>>>>>>>> ignored.
>>>>>>>
>>>>>>> So, you don't understand how logic works.
>>>>>>>
>>>>>>
>>>>>> It is because logic does not consistently know how correct reasoning
>>>>>> works. This correctly eliminates the principle of explosion:
>>>>>
>>>>> So, you are just proving you don't understand how logic works.
>>>>>
>>>>> You are proving your ignorance.
>>>>>
>>>>
>>>> The principle of explosion is self-evidently semantically incorrect.
>>>> Here is how to fix it: (A ∧ ¬A) := ε // empty string
>>>> thus (A ∧ ¬A) → B, B does not logically follow from the empty string.
>>>
>>> So, you don't understand the proof of the principle of explosion, as
>>> your example doesn't follow the form.
>>>
>>> You are just disproving a straw man
>>>
>>
>>
>> It is not that I do not understand the proof of the principle of
>> explosion. It is that I do understand that it derives nonsense.
>>
>> There is no semantic connection from lemons to unicorns thus making it
>> the non-sequitur error even if learned-by-rote logicians disagree.
>
> So, you don;t understand how logic works.

I understand how truth works thus can show where logic diverges from
truth thus making its inference incorrect.

The principle of explosion does diverge from correct reasoning.

>>
>> Logic is the woefully fallible human attempt at defining correct
>> reasoning and in some cases such as POE they missed the mark.
>>
>
> And either you use the system as defined, or start your own whole
> system, STARTING AT THE BEGFINNING.
>

I add foundational axioms in the upper ontology that ever logic system
must be based on or it diverges from correct reasoning:
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

> Changing the initial definition, and then starting at the far end is
> just an error, and shows you don't even understand your own rules (or
> are just a hypocrit and don't follow them),

The error is that no one every previously established the correct
foundation of analytic truth.

Tarski "proved" that it could not be done on the basis that Tarski could
not prove that a self-contradictory expression of language is true
within the same system that it was self-contradictory.
https://liarparadox.org/Tarski_275_276.pdf

G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
G is true if and only if G is unprovable and irrefutable in F
∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

within this foundational theorem
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/20/2022 10:56 AM, Richard Damon wrote:
> On 12/20/22 11:44 AM, olcott wrote:
>> On 12/18/2022 6:03 PM, Richard Damon wrote:
>>> On 12/18/22 10:28 AM, olcott wrote:
>>>
>>>> It may be the case "there is no finite proof of Goldbach's conjecture"
>>>> is true and unknowable because the answer requires an infinite proof.
>>>>
>>>
>>> Which means you accept that there may exist a statement (which
>>> actually allows for statements) that is actually TRUE but which can
>>> not be actually PROVEN and thus is unknowable.
>>>
>>> This is because proofs, by definition, are finite.
>>>
>>> Thus, you admit that your logic system might be incomplete.
>>>
>>
>> I never said that tracing through semantic connects had to be finite.
>> I only stipulated that when they do not exist then the expression of
>> language is not a truth bearer.
>
> So you accept that there is a diffence between something True and
> something Provable.
>

Unless and until an expression of language has been proven it is not an
element of the set of knowledge.

>>
>> Every element of the body of analytic truth is only true on the basis of
>> its semantic connections to other elements of the body of analytic
>> truth. Tracing through these connections is the proof of this truth.
>>
>>> In faxt, because of Godel's proof, which is similar, it is shown that
>>> it MUST be incomplete.
>>>
>>> How does it feel to admit that you whole work is proven wrong by your
>>> own words.
>>
>> "This sentence is not provable." Is not provable because it is
>> self-contradictory and has a vacuous truth object.
>
> But it is true, since no proof exists, something very demonstrable. The
> only issue is that the "proof" of the statement can only be done with a
> infintite search, or logic in a "meta-field" about the field.

G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
G is true if and only if G is unprovable and irrefutable in F
∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

within this foundational theorem
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

> This just shows you don't understand your own logic, or the definition
> of what a PROOF is.
>

To distinguish my ideas from the somewhat erroneous ideas of others my
system is called correct reasoning rather than any form of logic.

>>
>> This sentence is not true.
>> not true about what?
>> about being not true.
>> not true about being not true about what?
>>
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/20/2022 2:51 PM, Richard Damon wrote:
> On 12/20/22 11:52 AM, olcott wrote:
>> On 12/19/2022 12:20 PM, Richard Damon wrote:
>>> On 12/19/22 12:12 PM, olcott wrote:
>>>> On 12/19/2022 10:53 AM, Richard Damon wrote:
>>>>> On 12/19/22 10:33 AM, olcott wrote:
>>>>>
>>>>>> If every expression of language of analytical truth is only true
>>>>>> on the basis of its semantic connections to other elements of this
>>>>>> set then expressions of language that are true and unprovable
>>>>>> cannot possibly exist.
>>>>>>
>>>>>
>>>>> WHy do you say that?
>>>>>
>>>>> As I have said, Truth can exist from an INFINITE series of semantic
>>>>> connections, while proof requires a FINITE series of steps.
>>>>>
>>>>> All you are showing is that your mind doesn't comprehend the
>>>>> concepts of the infinite.
>>>>
>>>> Expressions of language are:
>>>> (1) True
>>>> (2) False
>>>> (3) Not truth bearers,
>>>> excluding all self contradictory expressions such as this:
>>>
>>> But actual self contradictory expressions just fall into your case
>>> (3), so aren't actually an excepting
>>>
>>>>
>>>> G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
>>>
>>> Which isn't G in F.
>>>
>>
>> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false
>
> That isn't G in F.
>
> G is actual a statement like
>
> There does not exist a Natural Number 'n' that satisfies the property R
> defined via a specfic primatitve recursive relationship (defined in the
> proof).
>
> The key point is that in the meta, it is shown that a number n that
> satisfies the property R encodes a proof of the statement G in F.

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

Gödel must use many pages of mathematical expressions to say that in the
language of arithmetic only because of its lack of expressiveness.

(G) F ⊢ GF ↔ ¬ProvF(┌GF┐).
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

Paraphrased as: ∃G ∈ F (G ↔ (F ⊬ G)) is simply false

within this foundational theorem
∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

>>
>> There exists a G in F such that it is true that G is neither provable
>> nor refutable in F.
>>
>> based on this foundational theorem (implied by Wittgenstein)
>> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>
>> 'True in Russell's system' means, as was said: proved in Russell's
>> system; and 'false in Russell's system' means: the opposite has been
>> proved in Russell's system. https://www.liarparadox.org/Wittgenstein.pdf
>
> Which since Russel's system doesn't use that definition of Truth, it is
> an inccorect statement, and the following is all unsound logic.
>

That Russel's system is ignorant of the way that truth really works does
not change how truth really works. Wittgenstein focused on the
philosophical underpinnings that everyone else simply ignored.

> That was just Wittgenstein making incorrect assumptions because of his
> own bias in logic.
>

*The definition of analytic statement requires this*
If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

> Which you repeat because you haven't learn from history, because you are
> just ignorant.
>
>>
>> Otherwise we have unprovable (the not a truth bearer) or unproven
>> (unknown truth value).
>>
>
> Which since you are using the wrong definition of G, apparently because
> of just using a bad knowledge of the cliff note versions of the
> description of Godel's theorem, your proof doesn't actual mean anything.

This convoluted mess requiring many pages of definitions
https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
is correctly summed up by this:

∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G)))

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/21/22 9:30 AM, olcott wrote:
> On 12/20/2022 10:41 AM, Richard Damon wrote:
>> On 12/20/22 11:08 AM, olcott wrote:
>>> On 12/18/2022 6:01 PM, Richard Damon wrote:
>>>
>>>> So, is the fact that a proof exist based on senses or not?
>>>>
>>>
>>> Do you need to taste or smell an arithmetic expression as a part of
>>> determining its value?
>>>
>>
>> So, you don't answer the question.
>>
>> Is the existance / non-existance of a proof determined by "senses" or
>> not.
>>
>
> The answer to the question was answered by my question.
> No it is not. Very obviously not.

So, since non-existance can require an infinite space search, while
proofs are required to be finite, you agree that analytic truth can be
based on an infinite chain of reasoning.

On the other hand, proofs that let us KNOW if something is true, require
a finite chain of reasoning.

>
>> Analytically, non-existence can require the use of an INFINITE number
>> of operations.
>>
>> Thus, the existance or non-existance of a proof is an actual FACT, but
>> might not be actually provable by a finite proof.
>
> OK so some things are unknown.

But still has a Truth Value.

>
>>>> If the mental process of searching the "space" of the system for a
>>>> proof is considered analytic, then the Collatz conjecture might be
>>>> provable false by finding a counter example, or it might be found
>>>> true because
>>>
>>> Yes.
>>
>> So you admit TRUTH can be based on an infinite number of steps, and
>> thus some TRUTH is not PROVABLE, because a proof must be finite.
>
> If an expression of language is true there must be a complete set of
> semantic connections making it true otherwise it is untrue.
>

But, as we showed above, that chain might be infinite in length, and
thus NOT a "Proof", which must be finite.

>>>
>>>> the infinte exhaustive search shoes that no such example exists.
>>>>
>>>> But an infinite search is NOT a valid proof, as a proof must have a
>>>> finite number of steps.
>>>>
>>>> There is NOTHING in your definition that requires a finite number of
>>>> steps to make a analytic expression true, only to be known.
>>>
>>> Since I am only dealing with true/false/neither the Collatz conjecture
>>> is outside the scope of this investigation. The Collatz conjecture is
>>> provably true or false by a finite or infinite proof thus meeting my
>>> requirements for True(x). Knowledge requires provably true or false by
>>> finite proof.
>>>
>>>
>>
>> The you logic can't handle the Natural Numbers by your own admission.
>>
>
> No human logic can possibly complete an infinite set of operations in
> finite time.

So, Truth is NOT based on humans being able to do the logic.

>
>> Your claim is that all Truth must be PROVABLE, not just determined by
>> an "infinite proof" (which is a oxymoron/contradictory statement).
>>
>
> If an expression of language is true there must be a complete set of
> semantic connections making it true otherwise it is untrue.

Which can be a INFINITE set of connections, and thus not a proof.

>
>> This is EXACTLY the same distinction that comes in the halting
>> problem, the TRUTH of Halting might come from an infinite number of
>> steps, but the Decider must answer in a finite number, so some
>> problems are not correctly decidable.

On 12/21/22 9:52 AM, olcott wrote:
> On 12/20/2022 10:41 AM, Richard Damon wrote:
>> On 12/20/22 10:43 AM, olcott wrote:
>>> On 12/18/2022 6:00 PM, Richard Damon wrote:
>>>> On 12/18/22 10:35 AM, olcott wrote:
>>>>> On 12/17/2022 11:33 AM, Richard Damon wrote:
>>>>>> On 12/17/22 12:25 PM, olcott wrote:
>>>>>>> On 12/16/2022 7:06 AM, Richard Damon wrote:
>>>>>>>> On 12/16/22 12:28 AM, Skep Dick wrote:
>>>>>>>>> On Friday, 16 December 2022 at 06:40:46 UTC+2,
>>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>>> Nope, you are showing you don't understand the difference
>>>>>>>>>> between Truth
>>>>>>>>>> and Knowledge, and thus unqualified to talk about them.
>>>>>>>>> Well, are you "qualified" to talk about them?
>>>>>>>>>
>>>>>>>>> You keep demonstrating (over and over) that if I gave you a bin
>>>>>>>>> full of Truth and non-Truth all mixed up together you don't
>>>>>>>>> know how to separate them.
>>>>>>>>>
>>>>>>>>> You don't know the (binary) classification rule for
>>>>>>>>> recognizing/separating/sorting Truth from non-Truth.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> But just asking someone to do that shows a lack of understanding
>>>>>>>> of the nature of Truth.
>>>>>>>>
>>>>>>>> Not all Truth is Known, or even Knowable, therefore no one has
>>>>>>>> the ability to completely sort every statement into the bins
>>>>>>>> True and False (or not True).
>>>>>>>
>>>>>>> Every element of the body of analytic truth is only true on the
>>>>>>> basis of
>>>>>>> its semantic connections to other elements of the body of analytic
>>>>>>> truth. Tracing through these connections is the proof of this truth.
>>>>>>>
>>>>>>> If these connections do not exist then an expression of language
>>>>>>> is not a truth bearer.
>>>>>>>
>>>>>>
>>>>>> Why? or maybe Why by this definition do you think it applies to
>>>>>> Mathematics?
>>>>>>
>>>>>> You are defining that "Expressions of Language" are true or not by
>>>>>> the meaning of their words.
>>>>>>
>>>>>> What in the meaning of the words"
>>>>>>
>>>>>
>>>>> Expressions of language that cannot possibly be shown to be true on
>>>>> the
>>>>> basis of their meaning are excluded form the body of analytic truth by
>>>>> definition.
>>>>
>>>>
>>>> The you must think that the Collatz Conjecture can not be an
>>>> analytic statement, as it can't b4 shown true (or false) just on the
>>>> meaning of the words.
>>>>
>>>
>>> I never said "meaning of words" please pay much more attention.
>>> I never said "meaning of words" please pay much more attention.
>>> I never said "meaning of words" please pay much more attention.
>>
>> You said, and I qoute:
>>> Expressions of language that cannot possibly be shown to be true on the
>>> basis of their meaning are excluded form the body of analytic truth by
>>> definition.
>>
>> What other meaning are you talking about then then meaning of the words.
>>
>
> You never heard of formal languages that do not use words?
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

And what are symbols other than words with a different alphabet?

>
>>> You replied to nine of my posts in four minutes.
>>
>> Right, I hold off sending until I review the lot, to see if you make a
>> statement elsewhere applicable.
>>
>>>
>>> The Collatz Conjecture is an expression of language with a currently
>>> unknown truth value, thus the existence of a finite set of semantic
>>> connections making it true or false is unknown. It cannot be currently
>>> considered unprovable it can only be considered unproven.
>>>
>>
>> So, do you admit that it IS a Truth Bearer? Even if it might be true
>> that it can NEVER be proven?
>>
>
> If an expression of language is true there must be a complete set of
> semantic connections making it true otherwise it is untrue.
>

Which might be infinite in length, so not a proof that makes it known.

>>>> That means MOST of Mathematics is "outside" this Analytical space
>>>> you are defining,
>>>
>>> Not at all and you cannot provide correct reasoning to support this.
>>
>> IF the Collatz conjecture might not be an "analytic statement" then it
>> shows that your logic can't handle math, as mathematics considers it a
>> valid statement that is True or False.
>>
>> If the Collatz conjecture IS accepted as an "analytic statement" even
>> if it might never be proven, then your assumption that all Truth is
>> provable is just shown to be FALSE.
>>
>
> If an analytic expression of language is true or false there must be a
> complete set of semantic connections making it true or false otherwise
> it is not a truth bearer.

But that chain can be an infinite chain, so not a proof that makes
something known (or knowable)

>
>> Which is it then, are the undetermined statements of Mathematics
>> outside the ability of your logic system to process, and thus your
>> logic system incapable of handling current Mathematics, or is your
>> statement that all Analytic Statements are by necessity provable false?
>>
>>>
>>>>>
>>>>>>> Every positive even integer can be written as the sum of two primes.
>>>>>>
>>>>>> Determines if this statement is True or not?
>>>>>>
>>>>>> It seems that it hangs on the EXISTANCE or not of an even number
>>>>>> that can't be expresses as the sum of two primes.
>>>>>>
>>>>>> To then say that it must be determinable by a FINITE sequence of
>>>>>> steps, is a contradiction of definitions.
>>>>>
>>>>> This is the border case. It is obvious that it is not currently an
>>>>> element of the body of analytic knowledge. It might be an element
>>>>> of the
>>>>> body of analytic truth or not depending on exactly what "possibly be
>>>>> shown to be true" means. I would say that because an infinite
>>>>> enumeration cannot possibly occur that it may not be a truth bearer.
>>>>>
>>>>
>>>> There is no "finite" connection limit on "Truth", only "Proof".
>>>>
>>>
>>> Any expression of language that is impossible to prove true or false
>>> is by definition not a truth bearer.
>>
>> FALSE.
>>
>> PROVE means a FINITE sequnence.
>> Some truth comes about from an INFINTE sequence of steps.
>>
>
> If an analytic expression of language is true or false there must be a
> complete set of semantic connections making it true or false otherwise
> it is not a truth bearer.

Which might be an infinitely large set, and thus not making it a proof
to make something known
>
>>>
>>> Examples:
>>> This sentence is not true.
>> Right, a contracdiction.
>>
>>> This sentence cannot be proven
>>
>> Which MUST be true, as if it was false then it means it COULD be
>> proven, and thus must be True.
>>
>> Note, Sentences of the form "x can be proven" or "x can not be proven"
>> are always Truth Bears as the proof either does or does not exist.
>>
>
> It is {truth bearer} not and animal with a furry body.

I though you were trying to point out sentences that were not truth bearers?

On 12/21/22 10:00 AM, olcott wrote:
> On 12/20/2022 10:41 AM, Richard Damon wrote:
>> On 12/20/22 11:25 AM, olcott wrote:
>>
>>> Within the foundation of analytical truth an expression of language is
>>> only true if it is either stipulated to be true or derived by applying
>>> truth preserving operations to expressions of language having the
>>> semantic property of Boolean true.
>>>
>>> Every element of the body of analytic truth is only true on the basis of
>>> its semantic connections to other elements of the body of analytic
>>> truth. Tracing through these connections is the proof of this truth.
>>>
>>> An expression of language that requires and infinite proof to show
>>> that it is true or false is a truth bearer with an unknown truth value.
>>
>> Which shows the differnce between Truth and Knowldge.
>>
>> Those things that require an infinite proof to indicate it is true,
>> are things that are True but Unprovable/unknowable, as Proofs, by
>> definition, are FINITE sequence of steps.
>>
>> If you want to allow infinite proofs in your system, you are using a
>> different language than everyone else, and need to change the term
>> "Unprovable" to "Unknowable" when reading otehr peoples work.
>>
>
> If an analytic expression of language is true or false there must be a
> complete set of semantic connections making it true or false otherwise
> it is not a truth bearer.

But it can be an infinite set, and thus not form a proof that lets the
value be known.

>
>> Incompleteness is essentially the assertion that there are some Truths
>> in the system that are not Provable (to you Knowable) in that system.
>>
>
> Therefore specifying this foundational theorem
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

Which is a FALSE assertion that all statements are provable or refutable
(if I am understanding your use of the symbols0

If you take that as an axiom, you have either limited your system to the
limited domain where that is true, or made your system inconsistent.

Note, incompleteness is a THERE EXIST sort of statement, your theorem is
a ALL sort of statement, so I don't see where incompleteness "specifies"
that theorem.

>
>> The problem with the term "Knowable" in this context is that generally
>> Knowability is allowed to leak between meta-systems and the system,
>> while provability is not.
>>
>
> I just addressed that. Based on the above foundational theorem:
> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

But was PROVEN true, for all F with at least a minimal set of
properties, so it shows that the systems based on your "foundational
theorem" either can't have those properties, or are, by definition,
inconsistent.

>
>> If we know something from a meta-system with correspondance to the
>> base system, we consider that we KNOW it, but that doesn't show
>> provablility in the system.
>>
>> So, allowing "Infinite Proofs" in your definitions reduces the
>> expresibility of your logic system.
>
> If an analytic expression of language is true or false there must be a
> complete set of semantic connections making it true or false otherwise
> it is not a truth bearer.
>

Yes. and that connection can be infinite in length, and thus not a
"Proof" that gives us knowledge.

On 12/21/22 10:42 AM, olcott wrote:
> On 12/20/2022 2:51 PM, Richard Damon wrote:
>> On 12/20/22 11:52 AM, olcott wrote:
>>> On 12/19/2022 12:20 PM, Richard Damon wrote:
>>>> On 12/19/22 12:12 PM, olcott wrote:
>>>>> On 12/19/2022 10:53 AM, Richard Damon wrote:
>>>>>> On 12/19/22 10:33 AM, olcott wrote:
>>>>>>
>>>>>>> If every expression of language of analytical truth is only true
>>>>>>> on the basis of its semantic connections to other elements of
>>>>>>> this set then expressions of language that are true and
>>>>>>> unprovable cannot possibly exist.
>>>>>>>
>>>>>>
>>>>>> WHy do you say that?
>>>>>>
>>>>>> As I have said, Truth can exist from an INFINITE series of
>>>>>> semantic connections, while proof requires a FINITE series of steps.
>>>>>>
>>>>>> All you are showing is that your mind doesn't comprehend the
>>>>>> concepts of the infinite.
>>>>>
>>>>> Expressions of language are:
>>>>> (1) True
>>>>> (2) False
>>>>> (3) Not truth bearers,
>>>>> excluding all self contradictory expressions such as this:
>>>>
>>>> But actual self contradictory expressions just fall into your case
>>>> (3), so aren't actually an excepting
>>>>
>>>>>
>>>>> G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
>>>>
>>>> Which isn't G in F.
>>>>
>>>
>>> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false
>>
>> That isn't G in F.
>>
>> G is actual a statement like
>>
>> There does not exist a Natural Number 'n' that satisfies the property
>> R defined via a specfic primatitve recursive relationship (defined in
>> the proof).
>>
>> The key point is that in the meta, it is shown that a number n that
>> satisfies the property R encodes a proof of the statement G in F.
>
> The conventional definition of incompleteness:
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Gödel must use many pages of mathematical expressions to say that in the
> language of arithmetic only because of its lack of expressiveness.

Nope, he does it so that he can express it in a way that ISN'T
self-referential in T, and thus you can't use that arguement to say it
is not a "truth bearer"

>
> (G) F ⊢ GF ↔ ¬ProvF(┌GF┐).
> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>
> Paraphrased as: ∃G ∈ F (G ↔ (F ⊬ G)) is simply false

Why?

>
> within this foundational theorem
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

Which isn't true, or causes such a system to be inconsistent.

>
>>>
>>> There exists a G in F such that it is true that G is neither provable
>>> nor refutable in F.
>>>
>>> based on this foundational theorem (implied by Wittgenstein)
>>> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>
>>> 'True in Russell's system' means, as was said: proved in Russell's
>>> system; and 'false in Russell's system' means: the opposite has been
>>> proved in Russell's system. https://www.liarparadox.org/Wittgenstein.pdf
>>
>> Which since Russel's system doesn't use that definition of Truth, it
>> is an inccorect statement, and the following is all unsound logic.
>>
>
> That Russel's system is ignorant of the way that truth really works does
> not change how truth really works. Wittgenstein focused on the
> philosophical underpinnings that everyone else simply ignored.

No, YOU are the one ignorant of the way that truth really works because
you mind it too small to actually comprehend it.

You can't explain your way out of the contradictions your logic creates,
because they are beyond your minds ability to even understand them.

>
>> That was just Wittgenstein making incorrect assumptions because of his
>> own bias in logic.
>>
>
> *The definition of analytic statement requires this*
> If an analytic expression of language is true or false there must be a
> complete set of semantic connections making it true or false otherwise
> it is not a truth bearer.

And it can be an INFINITE set of connections, and thus not forming a
proof that gives us knowledge, since that must be finite.

>
>> Which you repeat because you haven't learn from history, because you
>> are just ignorant.
>>
>>>
>>> Otherwise we have unprovable (the not a truth bearer) or unproven
>>> (unknown truth value).
>>>
>>
>> Which since you are using the wrong definition of G, apparently
>> because of just using a bad knowledge of the cliff note versions of
>> the description of Godel's theorem, your proof doesn't actual mean
>> anything.
>
> This convoluted mess requiring many pages of definitions
> https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
> is correctly summed up by this:
>
> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G)))
>

That is a paraphrase of G in the META theory that describes F.

In F, G is a sentence that MUST be a Truth Bearer, and thus if MUST be
one also in the meta theory,

Your claim otherwise just proves that you system in inconsistent because
you injected into it a FALSE theorem/axiom

On 12/21/22 10:12 AM, olcott wrote:
> On 12/20/2022 10:43 AM, Richard Damon wrote:
>> On 12/20/22 11:38 AM, olcott wrote:
>>> On 12/18/2022 6:03 PM, Richard Damon wrote:
>>>> On 12/18/22 10:23 AM, olcott wrote:
>>>>> On 12/17/2022 10:55 AM, Richard Damon wrote:
>>>>>> On 12/17/22 11:42 AM, olcott wrote:
>>>>>>> On 12/16/2022 6:16 PM, Richard Damon wrote:
>>>>>>>> On 12/16/22 10:34 AM, olcott wrote:
>>>>>>>>> On 12/15/2022 8:27 PM, Richard Damon wrote:
>>>>>>>>>> On 12/15/22 8:04 AM, Skep Dick wrote:
>>>>>>>>>>> On Thursday, 15 December 2022 at 14:59:36 UTC+2,
>>>>>>>>>>> richar...@gmail.com wrote:
>>>>>>>>>>>> Nope, because in mathematics with infinites you don't have
>>>>>>>>>>>> those properties.
>>>>>>>>>>>>
>>>>>>>>>>>> That is one of the problems with infinities.
>>>>>>>>>>>>
>>>>>>>>>>>> You are assuming that all the properties of the finite
>>>>>>>>>>>> numbers hold,
>>>>>>>>>>>> which they don't.
>>>>>>>>>>>
>>>>>>>>>>> Where's the objective arbiter on such things?
>>>>>>>>>>
>>>>>>>>>> That they generate contradictions, and thus make the system
>>>>>>>>>> worthless due to the power of the principle of explosion,
>>>>>>>>>> since there can be no actual information or knowledge in such
>>>>>>>>>> a system.
>>>>>>>>>
>>>>>>>>> The principle of explosion is incorrect because semantics are
>>>>>>>>> ignored.
>>>>>>>>
>>>>>>>> So, you don't understand how logic works.
>>>>>>>>
>>>>>>>
>>>>>>> It is because logic does not consistently know how correct reasoning
>>>>>>> works. This correctly eliminates the principle of explosion:
>>>>>>
>>>>>> So, you are just proving you don't understand how logic works.
>>>>>>
>>>>>> You are proving your ignorance.
>>>>>>
>>>>>
>>>>> The principle of explosion is self-evidently semantically incorrect.
>>>>> Here is how to fix it: (A ∧ ¬A) := ε // empty string
>>>>> thus (A ∧ ¬A) → B, B does not logically follow from the empty string.
>>>>
>>>> So, you don't understand the proof of the principle of explosion, as
>>>> your example doesn't follow the form.
>>>>
>>>> You are just disproving a straw man
>>>>
>>>
>>>
>>> It is not that I do not understand the proof of the principle of
>>> explosion. It is that I do understand that it derives nonsense.
>>>
>>> There is no semantic connection from lemons to unicorns thus making
>>> it the non-sequitur error even if learned-by-rote logicians disagree.
>>
>> So, you don;t understand how logic works.
>
> I understand how truth works thus can show where logic diverges from
> truth thus making its inference incorrect.
>
> The principle of explosion does diverge from correct reasoning.
>

Then your "logic" is different than the logic that is accepted for the
basis of Mathemematics, and thus not applicable to it.

You now need to show that your "New" definiton of Truth and Logic are
actually usable.

>>>
>>> Logic is the woefully fallible human attempt at defining correct
>>> reasoning and in some cases such as POE they missed the mark.
>>>
>>
>> And either you use the system as defined, or start your own whole
>> system, STARTING AT THE BEGFINNING.
>>
>
> I add foundational axioms in the upper ontology that ever logic system
> must be based on or it diverges from correct reasoning:
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

Nope, you don't get to do that.

You just don't have a correct definition of correct.

>
>> Changing the initial definition, and then starting at the far end is
>> just an error, and shows you don't even understand your own rules (or
>> are just a hypocrit and don't follow them),
>
> The error is that no one every previously established the correct
> foundation of analytic truth.

Nope, you just don't understand how logic works.

>
> Tarski "proved" that it could not be done on the basis that Tarski could
> not prove that a self-contradictory expression of language is true
> within the same system that it was self-contradictory.
> https://liarparadox.org/Tarski_275_276.pdf
>
> G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
> G is true if and only if G is unprovable and irrefutable in F
> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false
>
> within this foundational theorem
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>
>

Which is a FALSE theorem, as has actually been PROVEN, in any system
with sufficent power of reasoning.

All this shows is that you mental power is limited to the minor space of
logic where that can be taken as a basis of logic.

My understanding is this is a fairly well studied field, and not really
new, and its limits are fairly well known.

Your failure to learn from history has doomed you to repeating the
errors of the past.