On 5/14/22 11:32 AM, olcott wrote:
> On 5/14/2022 9:59 AM, Richard Damon wrote:
>> On 5/14/22 10:42 AM, olcott wrote:
>>> On 5/14/2022 8:42 AM, Richard Damon wrote:
>>>> On 5/14/22 12:01 AM, olcott wrote:
>>>>> On 5/13/2022 7:27 PM, Richard Damon wrote:
>>>>>> On 5/13/22 7:35 PM, olcott wrote:
>>>>>>> On 5/13/2022 6:22 PM, Richard Damon wrote:
>>>>>>>> On 5/13/22 7:05 PM, olcott wrote:
>>>>>>>>> On 5/13/2022 6:01 PM, Ben wrote:
>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>
>>>>>>>>>>> On 5/13/2022 3:46 PM, Ben wrote:
>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 5/13/2022 2:16 PM, Ben wrote:
>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> *Validity and Soundness*
>>>>>>>>>>>>>> Good plan.  You've run aground as far as halting is
>>>>>>>>>>>>>> concerned, so you
>>>>>>>>>>>>>> better find another topic you don't know about.
>>>>>>>>>>>>>
>>>>>>>>>>>>> It has been dead obvious that H(P,P)==0 is the correct halt
>>>>>>>>>>>>> status for
>>>>>>>>>>>>> the input to H(P,P) on the basis of the actual behavior
>>>>>>>>>>>>> that this
>>>>>>>>>>>>> input actually specifies.
>>>>>>>>>>>> It is now dead obvious that you accept that no algorithm can
>>>>>>>>>>>> do what the
>>>>>>>>>>>> world calls "decide halting".
>>>>>>>>>>>
>>>>>>>>>>> Tarski makes a similar mistake...
>>>>>>>>>>
>>>>>>>>>> <snip distractions>
>>>>>>>>>>
>>>>>>>>>>>>   That is, in the context of C-like code
>>>>>>>>>>>> that you are more comfortable with, no D can exist such that
>>>>>>>>>>>> D(X,Y) is
>>>>>>>>>>>> true if and only if X(Y) halts and is false otherwise.
>>>>>>>>>>>> Do you now accept that this is not possible?  (I know, I
>>>>>>>>>>>> know...  I
>>>>>>>>>>>> don't really expect an answer.)
>>>>>>>>>>
>>>>>>>>>> As expected, no answer.  You can't answer this because you
>>>>>>>>>> know that
>>>>>>>>>> would be the end of you bragging about halting.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> All undecidable problems always have very well hidden logical
>>>>>>>>> incoherence, false assumptions, or very well hidden gaps in
>>>>>>>>> their reasoning otherwise the fundamental nature of truth
>>>>>>>>> itself is broken.
>>>>>>>>>
>>>>>>>>
>>>>>>>> No, YOUR definition of truth gets proved to be inconsistent with
>>>>>>>> the system.
>>>>>>>>
>>>>>>>> If you want to insist that Truth must be Provable, then you need
>>>>>>>> to strictly limit the capabilities of your logic system.
>>>>>>>>
>>>>>>>> Your failure to understand this just shows you are a century
>>>>>>>> behind in the knowledge of how Truth and Logic actually works.
>>>>>>>
>>>>>>> The key thing here is not my lack of extremely in depth
>>>>>>> understanding of all of the subtle nuances of computer science.
>>>>>>>
>>>>>>> The key thing here is my much deeper understanding of how logic
>>>>>>> systems systems sometimes diverge from correct reasoning when
>>>>>>> examined at the very high level abstraction of the philosophical
>>>>>>> foundation of the notion of (analytic) truth itself.
>>>>>>>
>>>>>>> ittgensteinW had the exact same issue with mathematicians
>>>>>>> learned-by-rote by-the-book without the slightest inkling of any
>>>>>>> of the key philosophical underpinnings of these things, simply
>>>>>>> taking for granted that they are all these underpinnings are
>>>>>>> infallibly correct.
>>>>>>>
>>>>>>> When these underpinnings are incorrect this error is totally
>>>>>>> invisible to every learned-by-rote by-the-book mathematician.
>>>>>>>
>>>>>>
>>>>>> That other people have made the same errors, doesn't make you right.
>>>>>>
>>>>>> Note also, you are refering to a person who lived nearly that
>>>>>> century ago, to a man who admitted he didn't understand
>>>>>> mathematics (and thought it not valuable)
>>>>>>
>>>>>
>>>>> He refuted Godel in a single paragraph and was so far over
>>>>> everyone's head that they mistook his analysis for simplistic
>>>>> rather than most elegant bare essence.
>>>>
>>>> Nope, He made the same mistake YOU are making and not understanding
>>>> what Godel actually said (because he hadn't read the paper).
>>>>
>>>> As I understand it (and I will admit this isn't a field I have
>>>> intensly studied), this statement is solely from private notes that
>>>> were published after his death. If he really believed in this
>>>> statement as was sure of it, it would seem natural that he actually
>>>> would of published it.
>>>>
>>>> It seems likely that he had some nagging thought that there was an
>>>> error in his logic that he worked on and either never resolved or he
>>>> found his logic error and thus stopped believing in that statement.
>>>>
>>>
>>> Since I wrote Wittgenstein's entire same proof myself shortly before
>>> I ever heard of Wittgenstein I have first-hand direct knowledge that
>>> his reasoning is correct.
>>
>> No, you THINK his reasoning is correct because you agree with it,
>>
>
> No, I independently verified his reasoning before I ever saw his reasoning.
>
>> That is NOT proof. You thinking it is shows your lack of understanding.
>>
>>>
>>> His full quote is on page 6
>>> https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
>>>
>>>
>>> This is the key source of our agreement that makes Wittgenstein have
>>> the exact same view as mine:
>>>
>>>     '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.-
>>>
>>> True(x) iff Stipulated_True(x) or Proven_True(x)
>>
>> Which either needs to be taken as an assumption, or needs to be proved
>> to be true.
>>
>
> That no counter-examples can possibly exist is complete proof that it is
> true. There are no categories of expressions of language that are both
> true and neither stipulated as true or proven to be true (sound
> deduction) on the basis of semantic connections to other true
> expressions of language.

WRONG. Again you conflate Analytic truth with truth.

The Collatz conjecture, that there exist no number N such that the
sequence of progreesing to 3N+1 for N odd, and N/2 for N even doesn't
eventually reach 1, MUST be either True of False. There is no possible
"non-answer", as math doesn't allow for such things.

Thus either the statement "Collatz is True", or "Collatz is False", must
be true, and there is no known proof or refutation for either, While
this doesn't prove that no proof exists, it does point out a flaw with
your statement, until you have actually proved or refuted a statement,
you don't even know if it could be a truth bearer.

Thus we have a, at least possible, counter-example when you claim none
exist. You can only refute this as a possible counter-example by actualy
proving that a proof or refutation actually exists.

>
>> If needs to be taken as an assumption, it is not something that IS
>> unconditionally true.
>>
>>>
>>> There are only two possible ways that any ANALYTICALLY expression of
>>> language can possibly be true:
>>> (1) It is stipulated to be true. // like an axiom
>>> (2) It is derived by applying only truth preserving operations to (1)
>>> or the consequences of (2).         // like sound deduction
>>
>> WRONG.
>>
>> There are only two possible ways that they can be ANALYTICALLY true.
>>
>
> Should I capitalize my use of ANALYTICALLY too so that you can see that
> I already specified this? (I capitalized it, above)

Except then it points out that you erroeous omit it in your other
statements.
>
>>>
>>> Analytic truth includes every expression of language that can be
>>> completely verified as totally true entirely on the basis of its
>>> meaning without requiring any sense data from the sense organs.
>>
>> And there are other truths besides Analytic Truth. That is implied by
>> the need of the adjective.
>
> All of math and logic is exclusively ANALYTICAL.

That is part of your error. Math and Logic use analytical methods to
prove its ideas, but not all Truth in math and logic is Analytical.

>
>>>
>>> Empirical expressions of language also require sense data from the
>>> sense organs to verify their truth.
>>
>> Nope, things can be empirically true even without the sense data.
>> Without the sense data they are not KNOWN to be true, but might be.
>>
>
> to verify their truth.
> to verify their truth.
> to verify their truth.

Truth doesn't need to be "Verified" to be True. It only needs to be
verified before its Truth can be used to create other Truths in a Proof.

>
>>>
>>> This means that if there are no connected set of semantics meanings
>>> (sound deduction) that make an analytical expression of language true
>>> then then it cannot possibly be true unless it was stipulated as true.
>>
>> WRONG. You are again confalating KNOWLEDGE with TRUTH.
>
> Counter-examples are categorically impossible because ALL ANALYTIC
> expressions of language ONLY derive their truth value from semantic
> connections to other ANALYTIC expressions of language that are known to
> be true, AKA sound deduction.
>

Thus, the circular definition.

You only show that ANALYTIC Truth must be proven, not Truth.

Analytics accept that not all Truth is Analytically proven. You make a
category error assuming all Truth must be Analytically True.

Note, An Analytical Statement might be True but not Analytically ture.
>
>>>
>>> The conclusion of Wittgenstein's analysis and mind is that if G is
>>> unprovable in F then G is simply untrue in F.
>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)).
>>
>> WRONG.
>>
>> Makes the erroneous assumption that Truth requires proof, and becomes
>> a circular argument.
>
> It is not a circle it is a tree of sound deduction.
> The conclusion is linked backwards (sound deduction in reverse) to every
> expression of language that derives it.

Nope. Give the NON-CIRCULAR proof.

Your failure to show what you claim is evidence that you don't actually
have a real proof.

Your statement that "Something is True only if it is Provable" is itself
a contradiction unless you can ACTUALLY prove it, and until you do, you
can not use it.

Without such a proof, the statement says it can not be true, so you can
not use it.

>
>>
>>>
>>> Even though F does meet the erroneous mathematical definition of
>>> Incomplete(F) that F was ever construed as incomplete is simply
>>> incorrect because it does not screen out expressions of language that
>>> are simply not truth bearers.
>>
>> Except that the expression of language WAS a Truth Bearer, as a given
>> statement MUST be either Provable or not. This comes because you of
>> course can't prove an statement that can't be true, like a non-sense
>> sentence.
>>
>
> As recently as 1974, people were still clueless about the issue of the
> liar paradox.It is the simplest of all self-reference paradoxes so I
> bought the domain name liarparadox.org for my work.
>
> Tarski based his whole proof on the liar paradox and proved in his
> metatheory that it is not provable in his theory, same result as Godel.
>
>> Unless you are willing to define that Provability isn't a Truth
>> Bearer, which since you are then defining Truth as Provable, the Truth
>> of a statement isn't a Truth Bearer, you have a problem. You whole
>> logic system collapses as it can no longer talk about itself.
>>
>
> True(F, x) is implemented as Provable(F, x) through sound deduction on
> the basis of premises known to be true. In a reverse sound deduction
> (same thing as Prolog back-chaining inference) know truths (AKA Prolog
> facts) are sought on the basis of Prolog rules.
>
> https://www.google.com/search?q=prolog+back+chainikng&rlz=1C1GCEJ_enUS813US813&oq=prolog+back+chainikng&aqs=chrome..69i57j33i10i160.4658j0j15&sourceid=chrome&ie=UTF-8
>
>

And Prolog doesn't define logic, but is just a programming languge to
handle simple rule sets.

Note, Prolog doesn't provide a well implemented "Not" operator, in part
BECAUSE it defines a statement that is unprovable as false.

If you want to limit your logic to what Prolog can handle, be my guess,
but then stay out of things beyond its capability, like Compuation Theory.

I don't think you are smart enough to understand the limitation of
Prolog (or even simple logic) and thus make enormous errors not
understanding the limited domain of your tools.

You just don't see that you logic system has become horribly
inconsistent because you close your eyes to those errors and say that
logic must be wrong, but you can't actually define WHAT is wrong with
the logic, because it actually does follow the rules you propose.

>>
>>>
>>> Tarski made this same mistake with a much simply yet comparable proof
>>> to the Gödel 1931 incompleteness theorem:
>>> Tarski undefinability theorem 1936
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>>     "the sentence x which is undecidable in the original theory
>>>     becomes a decidable sentence in the enriched theory."
>>>
>>> It is not that Tarski's metatheory is smarter than his theory.
>>> It is that Tarski's x (the liar paradox) is not provable or true in
>>> his theory because it is not a truth bearer in his theory in the same
>>> way that Gödel's G is not a truth bearer in F.
>>>
>>>> This make the "appeal" to him as an authority to rebut Godel
>>>> incorrect, as he never stood as an authority to make such a claim,
>>>> he just investigated it in private notes.
>>>>
>>>> Perhaps he realized that his argument to try to prove that Truth can
>>>> be proven rested on the assumption of a definition that Truth was
>>>> Provable and thus is just a circular argument.
>>>>
>>>> As I have put to you, PROVE that Truth must be Provable, or by your
>>>> own logic the statement isn't true. We KNOW (if we have any
>>>> intelligence) that there are Truths that we do not know about, so it
>>>> is established that some truths are at least unknown for now. What
>>>> is the basis for saying that there can't be an aspect that happens
>>>> to be true even though we can not prove it?
>>>>
>>>>
>>>>>
>>>>>> You aseem to be refering to writings published post-humously about
>>>>>> a his comments on a paper he hadn't yet actually read, and that he
>>>>>> never repeated after actually reading the paper.
>>>>>>
>>>>>> Yes, that is very good basis for claiming your idea have to be right.
>>>>>>
>>>>>> You have shown ZERO understanding for the rules of logic, and that
>>>>>> your opinions are basically worthless.
>>>>>>
>>>>>> If you want to try to ACTUAL PROVE something, based on REAL
>>>>>> ESTABLISHED rules of logic, go ahead and give a try.
>>>>>>
>>>>>> Note, this means NOT just falling back to "the meaning of the
>>>>>> words" except when you are actually QUOTING the accepted meaning
>>>>>> of those words in the field and showing how they apply.
>>>>>>
>>>>>> I don't know if I have ever seen you put together a string of
>>>>>> logic more that one or two steps before you go off on a "this must
>>>>>> be true" side track, and never actually use any of the fundamental
>>>>>> definitions. (You may quotes some of them, but then never actually
>>>>>> use that definition in your nest step of the proof).
>>>>>
>>>>>
>>>>
>>>
>>>
>>
>
>