On 4/26/23 2:07 AM, olcott wrote:
> On 4/25/2023 6:56 AM, Richard Damon wrote:
>> On 4/25/23 12:03 AM, olcott wrote:
>>> On 4/24/2023 6:35 PM, Richard Damon wrote:
>>>> On 4/24/23 11:25 AM, olcott wrote:
>>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making
>>>>>>>>>>>>>>> it erroneous.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>>
>>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps
>>>>>>>>>>>>> in F that
>>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>>
>>>>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>>>>> true but not provable in F.
>>>>>>>>>>>>
>>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>>
>>>>>>>>>>> To prove G in F you do.
>>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, you don't understand how to prove that something is "True
>>>>>>>>>> in F" by doing the steps in Meta-F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>>
>>>>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>>>>> then the Liar's paradox would be true, thus that assumption can
>>>>>>>> not be true.
>>>>>>>>
>>>>>>>
>>>>>>> When one level of indirect reference is applied to the Liar
>>>>>>> Paradox it
>>>>>>> becomes actually true. There was no "if".
>>>>>>>
>>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>>
>>>>>>>> Your
>>>>>>>>
>>>>>>>>>
>>>>>>>>> We can do the same thing when G asserts its own unprovability
>>>>>>>>> in F.
>>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>>> inference
>>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>>
>>>>>>>> Right, you can't prove, in F, that G is true, but you can prove,
>>>>>>>> in Meta-F, that G is true in F, and that G is unprovable in F,
>>>>>>>> which is what is required.
>>>>>>>>
>>>>>>>
>>>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>>>> because this requires a sequence of inference steps in F that
>>>>>>> prove that
>>>>>>> they themselves do not exist.
>>>>>>>
>>>>>>> Meta-F merely removes the self-contradiction the same way
>>>>>>> Tarski's Meta-
>>>>>>> theory removed the self-contradiction.
>>>>>>>
>>>>>>>
>>>>>>>> You are just showing that your mind can't handle the basics of
>>>>>>>> logic, or truth.
>>>>>>>>
>>>>>>>
>>>>>>> It may seem that way to someone that learns things by rote and
>>>>>>> mistakes
>>>>>>> this for actual understanding of exactly how all of the elements
>>>>>>> of a
>>>>>>> proof fit together coherently or fail to do so.
>>>>>>>
>>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>>
>>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>>> just don't any better.
>>>>>>>>
>>>>>>>
>>>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>>>
>>>>>>> Learning the details of these things could have boxed me into a
>>>>>>> corner
>>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>>> elements
>>>>>>> fail to fit together coherently.
>>>>>>>
>>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>>> semantic
>>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>>> foundation
>>>>>>> cannot be incomplete nor have any expressions of language that are
>>>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>>>> exactly
>>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>>
>>>>>>>>>
>>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>>>> cannot be
>>>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot
>>>>>>>>> be proved in Tarski's theory.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Which he didn't do, but you are too stupid to understand
>>>>>>>> claissic arguement forms.
>>>>>>>>
>>>>>>>
>>>>>>> It is not that I do not understand, it is that I can directly see
>>>>>>> where and how formal mathematical systems diverge from correct
>>>>>>> reasoning.
>>>>>>
>>>>>> But since you are discussing Formal Logic, you need to use the
>>>>>> rules of Formal logic.
>>>>>>
>>>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>>>> from the accepted and proven system of Formal Logic.
>>>>>
>>>>>
>>>>>
>>>>> In classical logic, intuitionistic logic and similar logical
>>>>> systems, the principle of explosion
>>>>>
>>>>> ex falso [sequitur] quodlibet,
>>>>> 'from falsehood, anything [follows]'
>>>>>
>>>>> ex contradictione [sequitur] quodlibet,
>>>>> 'from contradiction, anything [follows]')
>>>>
>>>> Right, if a logic system can prove a contradiction, that out of that
>>>> contradiction you can prove anything
>>>>
>>>>>
>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>
>>>>> ∴ FALSE ⊢ Donald Trump is the Christ
>>>>> ∴ FALSE ⊢ Donald Trump is Satan
>>>>
>>>> Which isn't what was being talked about.
>>>>
>>>> You clearly don't understand how the principle of explosion works,
>>>> which isn't surprising considering how many misconseptions you have
>>>> about how logic works.
>>>>
>>>
>>> ex falso [sequitur] quodlibet,'from falsehood, anything [follows]'
>>> ∴ FALSE ⊢ Donald Trump is the Christ
>>
>> But you are using the wrong symbol
>>
>>
>
> 'from falsehood, anything [follows]'
> FALSE Proves that Donald Trump is the Christ

On 4/26/23 12:38 AM, olcott wrote:
> On 4/25/2023 6:56 AM, Richard Damon wrote:
>> On 4/24/23 11:28 PM, olcott wrote:
>>> On 4/24/2023 6:35 PM, Richard Damon wrote:
>>>> On 4/24/23 12:13 PM, olcott wrote:
>>>>> On 4/24/2023 10:58 AM, olcott wrote:
>>>>>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 7:57 PM, olcott wrote:
>>>>>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> G is unprovable because it is self-contradictory,
>>>>>>>>>>>>>>>>>> making it erroneous.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Any proof of G in F requires a sequence of inference
>>>>>>>>>>>>>>>> steps in F that
>>>>>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is of course impossible to prove in F that a statement
>>>>>>>>>>>>>>> is true but not provable in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> To prove G in F you do.
>>>>>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>>>>>> This sentence is not true: "This sentence is not true" is
>>>>>>>>>>>>>> true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So, you don't understand how to prove that something is
>>>>>>>>>>>>> "True in F" by doing the steps in Meta-F.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>>>>>
>>>>>>>>>>> No, he didn't, he showed that *IF* a certain assuption was
>>>>>>>>>>> true, then the Liar's paradox would be true, thus that
>>>>>>>>>>> assumption can not be true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When one level of indirect reference is applied to the Liar
>>>>>>>>>> Paradox it
>>>>>>>>>> becomes actually true. There was no "if".
>>>>>>>>>>
>>>>>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>>>>>
>>>>>>>>>>> Your
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> We can do the same thing when G asserts its own
>>>>>>>>>>>> unprovability in F.
>>>>>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>>>>>> inference
>>>>>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>>>>>
>>>>>>>>>>> Right, you can't prove, in F, that G is true, but you can
>>>>>>>>>>> prove, in Meta-F, that G is true in F, and that G is
>>>>>>>>>>> unprovable in F, which is what is required.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When G asserts its own unprovability in F it cannot be proved
>>>>>>>>>> in F
>>>>>>>>>> because this requires a sequence of inference steps in F that
>>>>>>>>>> prove that
>>>>>>>>>> they themselves do not exist.
>>>>>>>>>>
>>>>>>>>>> Meta-F merely removes the self-contradiction the same way
>>>>>>>>>> Tarski's Meta-
>>>>>>>>>> theory removed the self-contradiction.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> You are just showing that your mind can't handle the basics
>>>>>>>>>>> of logic, or truth.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It may seem that way to someone that learns things by rote and
>>>>>>>>>> mistakes
>>>>>>>>>> this for actual understanding of exactly how all of the
>>>>>>>>>> elements of a
>>>>>>>>>> proof fit together coherently or fail to do so.
>>>>>>>>>>
>>>>>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>>>>>> intentionaally hamstrung yourself to avoid being "polluted"
>>>>>>>>>>> by "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>>>>>
>>>>>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>>>>>> just don't any better.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I do at this point need to understand model theory very
>>>>>>>>>> thoroughly.
>>>>>>>>>>
>>>>>>>>>> Learning the details of these things could have boxed me into
>>>>>>>>>> a corner
>>>>>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>>>>>> elements
>>>>>>>>>> fail to fit together coherently.
>>>>>>>>>>
>>>>>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>>>>>> semantic
>>>>>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>>>>>> foundation
>>>>>>>>>> cannot be incomplete nor have any expressions of language that
>>>>>>>>>> are
>>>>>>>>>> undecidable. Now that I have this foundation I have a way to
>>>>>>>>>> see exactly
>>>>>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY
>>>>>>>>>>>> G cannot be
>>>>>>>>>>>> proved in F. G cannot be proved in F for the same
>>>>>>>>>>>> pathological self-reference(Olcott 2004) reason that the
>>>>>>>>>>>> Liar Paradox cannot be proved in Tarski's theory.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Which he didn't do, but you are too stupid to understand
>>>>>>>>>>> claissic arguement forms.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is not that I do not understand, it is that I can directly
>>>>>>>>>> see where and how formal mathematical systems diverge from
>>>>>>>>>> correct reasoning.
>>>>>>>>>
>>>>>>>>> But since you are discussing Formal Logic, you need to use the
>>>>>>>>> rules of Formal logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I have never been talking about formal logic. I have always been
>>>>>>>> talking
>>>>>>>> about the philosophical foundations of correct reasoning.
>>>>>>>
>>>>>>> No, you have been talking about theorys DEEP in formal logic. You
>>>>>>> can't talk about the "errors" in those theories, with being in
>>>>>>> formal logic.
>>>>>>>
>>>>>>> IF you think you can somehow talk about the foundations, while
>>>>>>> working in the penthouse, you have just confirmed that you do not
>>>>>>> understand how ANY form of logic works.
>>>>>>>
>>>>>>> PERIOD.
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>>> The other way to say it is that your "Correct Reasoning"
>>>>>>>>> diverges from the accepted and proven system of Formal Logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is correct reasoning in the absolute sense that I refer to.
>>>>>>>> If anyone has the opinion that arithmetic does not exist they are
>>>>>>>> incorrect in the absolute sense of the word: "incorrect".
>>>>>>>>
>>>>>>>
>>>>>>> IF you reject the logic that a theory is based on, you need to
>>>>>>> reject the logic system, NOT the theory.
>>>>>>>
>>>>>>> You are just showing that you have wasted your LIFE because you
>>>>>>> don'tunderstnad how to work ligic.
>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Because you are a learned-by-rote person you make sure to
>>>>>>>>>> never examine
>>>>>>>>>> whether or not any aspect of math diverges from correct
>>>>>>>>>> reasoning, you
>>>>>>>>>> simply assume that math is the gospel even when it contradicts
>>>>>>>>>> itself.
>>>>>>>>>
>>>>>>>>> Nope, I know that with logic, if you follow the rules, you will
>>>>>>>>> get the correct answer by the rules.
>>>>>>>>>
>>>>>>>>> If you break the rules, you have no idea where you will go.
>>>>>>>>>
>>>>>>>>
>>>>>>>> In other words you never ever spend any time on making sure that
>>>>>>>> these
>>>>>>>> rules fit together coherently.
>>>>>>>
>>>>>>> The rules work together just fine.
>>>>>>>
>>>>>>> YOU don't like some of the results, but they work just fine for
>>>>>>> most of the field.
>>>>>>>
>>>>>>> You are just PROVING that you have no idea how to actually
>>>>>>> discuss a new foundation for logic, likely because you are
>>>>>>> incapable of actually comeing up with a consistent basis for
>>>>>>> working logic.
>>>>>>>
>>>>>>>>
>>>>>>>>> As I have told you before, if you want to see what your
>>>>>>>>> "Correct > Reasoning" can do as a replaceent logic system, you
>>>>>>>>> need to start at the
>>>>>>>>> BEGINNING, and see wht it gets.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The foundation of correct reasoning is that the entire body of
>>>>>>>> analytical truth is a set of semantic tautologies.
>>>>>>>>
>>>>>>>> This means that all correct inference always requires
>>>>>>>> determining the
>>>>>>>> semantic consequence of expressions of language. This semantic
>>>>>>>> consequence can be specified syntactically, and indeed must be
>>>>>>>> represented syntactically to be computable
>>>>>>> Meaningless gobbledy-good until you actually define what you mean
>>>>>>> and spell out the actual rules that need to be followed.
>>>>>>>
>>>>>>> Note, "Computability" is actually a fairly late in the process
>>>>>>> concept. You first need to show that you logic can actually do
>>>>>>> something useful
>>>>>>>
>>>>>>>>
>>>>>>>>> To just try to change things at the end is just PROOF that your
>>>>>>>>> "Correct Reasoning" has to not be based on any real principles
>>>>>>>>> of logic.
>>>>>>>>>
>>>>>>>>> Since it is clear that you want to change some of the basics of
>>>>>>>>> how logic works, you are not allowed to just use ANY of
>>>>>>>>> classical logic until you actually show what part of it is
>>>>>>>>> still usable under your system and what changes happen.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Whenever an expression of language is derived as the semantic
>>>>>>>> consequence of other expressions of language we have valid
>>>>>>>> inference.
>>>>>>>
>>>>>>> And, are you using the "classical" definition of "semantic"
>>>>>>> (which makes this sentence somewhat cirular) or do you mean
>>>>>>> something based on the concept you sometimes use of  "the meaning
>>>>>>> of the words".
>>>>>>>
>>>>>>
>>>>>> *Principle of explosion*
>>>>>> An alternate argument for the principle stems from model theory. A
>>>>>> sentence P is a semantic consequence of a set of sentences Γ only if
>>>>>> every model of Γ is a model of P. However, there is no model of the
>>>>>> contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
>>>>>> that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P)
>>>>>> is a
>>>>>> model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>
>>>>>> Vacuous truth does not count as truth.
>>>>>> All variables must be quantified
>>>>>>
>>>>>> "all cell phones in the room are turned off" will be true when no
>>>>>> cell phones are in the room.
>>>>>>
>>>>>> ∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))
>>>>>>
>>>>>>
>>>>>>>>
>>>>>>>> The semantic consequence must be specified syntactically so that
>>>>>>>> it can
>>>>>>>> be computed or examined in formal systems.
>>>>>>>>
>>>>>>>> Just like in sound deductive inference when the premises are
>>>>>>>> known to be
>>>>>>>> true, and the reasoning valid (a semantic consequence) then the
>>>>>>>> conclusion is necessarily true.
>>>>>>>
>>>>>>> So, what is the difference in your system from classical Formal
>>>>>>> Logic?
>>>>>>>
>>>>>>
>>>>>> Semantic Necessity operator: ⊨□
>>>>>>
>>>>>>     FALSE ⊨□ FALSE // POE abolished
>>>>>> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>>>>>>
>>>>>> ⇒ and → symbols are replaced by ⊨□
>>>>>>
>>>>>> The sets that the variables range over must be defined
>>>>>> all variables must be quantified
>>>>>>
>>>>>> // x is a semantic consequence of its premises in L
>>>>>> Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)
>>>>>>
>>>>>> // x is a semantic consequence of the axioms of L
>>>>>> True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)
>>>>>>
>>>>>> *The above is all that I know right now*
>>>>>>
>>>>>>
>>>>>>>> The most important aspect of the tiny little foundation of a formal
>>>>>>>> system that I already specified immediately above is self-evident:
>>>>>>>> True(L,X) can be defined and incompleteness is impossible.
>>>>>>>
>>>>>>> I don't think your system is anywhere near establish far enough
>>>>>>> for you to say that.
>>>>>>
>>>>>> Try and show exceptions to this rule and I will fill in any gaps that
>>>>>> you find.
>>>>>>
>>>>>> G asserts its own unprovability in F
>>>>>> The reason that G cannot be proved in F is that this requires a
>>>>>> sequence of inference steps in F that proves no such sequence
>>>>>> of inference steps exists in F.
>>>>>>
>>>>>>
>>>>> ∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
>>>>> ∄sequence_of_inference_steps ⊆ F)
>>>>>
>>>>>
>>>>
>>>> So, you don't understand the differnce between the INFINITE set of
>>>> sequence steps that show that G is True, and the FINITE number of
>>>> steps that need to be shown to make G provable.
>>>>
>>>
>>> The experts seem to believe that unless a proof can be transformed into
>>> a finite sequence of steps it is no actual proof at all. Try and cite a
>>> source that says otherwise.
>>
>> WHy? Because I agree with that. A Proof needs to be done in a finite
>> number of steps.
>>
>> The question is why the infinite number of steps in F that makes G
>> true don't count for making it true.
>>
>> Yes, you can't write that out to KNOW it to be true, but that is the
>> differece between knowledge and fact.
>>
>
> Infinite proof are not allowed: Because they can't possibly ever occur.
>
>>>
>>> We can imagine an Oracle machine that can complete these proofs in the
>>> same sort of way that we can imagine a magic fairy that waves a magic
>>> wand.
>>>
>>>> You are just showing you don't understand what you talking about and
>>>> just spouting word (or symbol) salad.
>>>>
>>>> You are oriving you are an IDIOT.
>>>
>>> I am seeing these things at a deeper philosophical level than you
>>> are. I know that is hard to believe.
>>
>> But not according to the rules of the system you are talking about.
>>
>> You don't get to change the rules on a system.
>>
>
> YES I DO !!!
> My whole purpose to provide the *correct reasoning* foundation such that
> formal systems can be defined without undecidability or undefinability,
> or inconsistently.

On 4/16/2023 6:16 AM, Richard Damon wrote:
> On 4/15/23 10:54 PM, olcott wrote:
>
>> G is unprovable because it is self-contradictory, making it erroneous.
>>
>
> Since you don't understand the meaning of self-contradictory, that claim
> is erroneous.
>

When G asserts its own unprovability in F:

Any proof of G in F requires a sequence of inference steps in F that
prove that they themselves do not exist in F.

This is precisely analogous to you proving that you yourself never
existed.

> You are also working with a Strawman, because you can't understand the
> actual statement G, so even if you were right about the statement you
> are talking about, you would still be wrong about the actual statement.
>
> The ACTUAL G has no "Self-Reference" in it, so can't be
> "Self-Contradictory".
>
> You are just proving how ignorant you are of logic.
>

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/23 5:08 PM, olcott wrote:
> On 4/16/2023 6:16 AM, Richard Damon wrote:
>> On 4/15/23 10:54 PM, olcott wrote:
>>
>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>
>>
>> Since you don't understand the meaning of self-contradictory, that
>> claim is erroneous.
>>
>
> When G asserts its own unprovability in F:

But Godel's G doesn't do that.

>
> Any proof of G in F requires a sequence of inference steps in F that
> prove that they themselves do not exist in F.

It is of course impossible to prove in F that a statement is true but
not provable in F.

You don't need to do the proof in F, Godel shows how to construct a
Meta-F system from F that allows construction a proof IN META-F that
shows that his G is True in F, and not provable in F.

>
> This is precisely analogous to you proving that you yourself never
> existed.

Nope, you are just proving you can't do your strawman, because you have
straw for brains.

You start from an incorrect assertion, that G actually asserts its own
unprovability, and then continue to make errors in asserting that this
is proven in F itself.

This just shows you fundamentally don't understand how the logic works,
and that you are too stupid to be able to be taught it.

On 4/22/2023 4:27 PM, Richard Damon wrote:
> On 4/22/23 5:08 PM, olcott wrote:
>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>> On 4/15/23 10:54 PM, olcott wrote:
>>>
>>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>>
>>>
>>> Since you don't understand the meaning of self-contradictory, that
>>> claim is erroneous.
>>>
>>
>> When G asserts its own unprovability in F:
>
> But Godel's G doesn't do that.
>
>>
>> Any proof of G in F requires a sequence of inference steps in F that
>> prove that they themselves do not exist in F.
>
> It is of course impossible to prove in F that a statement is true but
> not provable in F.
>
> You don't need to do the proof in F,

To prove G in F you do.
Otherwise you are doing the same cheap trick as Tarski:
This sentence is not true: "This sentence is not true" is true.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/23 5:36 PM, olcott wrote:
> On 4/22/2023 4:27 PM, Richard Damon wrote:
>> On 4/22/23 5:08 PM, olcott wrote:
>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>
>>>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>>>
>>>>
>>>> Since you don't understand the meaning of self-contradictory, that
>>>> claim is erroneous.
>>>>
>>>
>>> When G asserts its own unprovability in F:
>>
>> But Godel's G doesn't do that.
>>
>>>
>>> Any proof of G in F requires a sequence of inference steps in F that
>>> prove that they themselves do not exist in F.
>>
>> It is of course impossible to prove in F that a statement is true but
>> not provable in F.
>>
>> You don't need to do the proof in F,
>
> To prove G in F you do.
> Otherwise you are doing the same cheap trick as Tarski:
> This sentence is not true: "This sentence is not true" is true.
>
>

So, you don't understand how to prove that something is "True in F" by
doing the steps in Meta-F.

Just shows you are ignorant.

Too bad you are going to die in such disgrace.

All you need to do is show that there exist a (possibly infinte) set of
steps from the truth makers in F, using the rules of F, to G. Youy don't
need to actually DO this in F, if you have a system that knowns about F.

Your mind is just too small.

On 4/22/2023 4:54 PM, Richard Damon wrote:
> On 4/22/23 5:36 PM, olcott wrote:
>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>> On 4/22/23 5:08 PM, olcott wrote:
>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>
>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>> erroneous.
>>>>>>
>>>>>
>>>>> Since you don't understand the meaning of self-contradictory, that
>>>>> claim is erroneous.
>>>>>
>>>>
>>>> When G asserts its own unprovability in F:
>>>
>>> But Godel's G doesn't do that.
>>>
>>>>
>>>> Any proof of G in F requires a sequence of inference steps in F that
>>>> prove that they themselves do not exist in F.
>>>
>>> It is of course impossible to prove in F that a statement is true but
>>> not provable in F.
>>>
>>> You don't need to do the proof in F,
>>
>> To prove G in F you do.
>> Otherwise you are doing the same cheap trick as Tarski:
>> This sentence is not true: "This sentence is not true" is true.
>>
>>
>
> So, you don't understand how to prove that something is "True in F" by
> doing the steps in Meta-F.
>

I just showed you how Tarski proved that the Liar Paradox expressed in
his theory is true in his meta-theory.

We can do the same thing when G asserts its own unprovability in F.
G cannot be proved in F because this requires a sequence of inference
steps in F that prove that they themselves do not exist in F.

You and I can see both THAT G cannot be proved in F and WHY G cannot be
proved in F. G cannot be proved in F for the same pathological
self-reference(Olcott 2004) reason that the Liar Paradox cannot be
proved in Tarski's theory.

> Just shows you are ignorant.
>
> Too bad you are going to die in such disgrace.
>
> All you need to do is show that there exist a (possibly infinte) set of
> steps from the truth makers in F, using the rules of F, to G. Youy don't
> need to actually DO this in F, if you have a system that knowns about F.
>
> Your mind is just too small.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/23 6:10 PM, olcott wrote:
> On 4/22/2023 4:54 PM, Richard Damon wrote:
>> On 4/22/23 5:36 PM, olcott wrote:
>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>
>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>> erroneous.
>>>>>>>
>>>>>>
>>>>>> Since you don't understand the meaning of self-contradictory, that
>>>>>> claim is erroneous.
>>>>>>
>>>>>
>>>>> When G asserts its own unprovability in F:
>>>>
>>>> But Godel's G doesn't do that.
>>>>
>>>>>
>>>>> Any proof of G in F requires a sequence of inference steps in F that
>>>>> prove that they themselves do not exist in F.
>>>>
>>>> It is of course impossible to prove in F that a statement is true
>>>> but not provable in F.
>>>>
>>>> You don't need to do the proof in F,
>>>
>>> To prove G in F you do.
>>> Otherwise you are doing the same cheap trick as Tarski:
>>> This sentence is not true: "This sentence is not true" is true.
>>>
>>>
>>
>> So, you don't understand how to prove that something is "True in F" by
>> doing the steps in Meta-F.
>>
>
> I just showed you how Tarski proved that the Liar Paradox expressed in
> his theory is true in his meta-theory.

No, he didn't, he showed that *IF* a certain assuption was true, then
the Liar's paradox would be true, thus that assumption can not be true.

Your

>
> We can do the same thing when G asserts its own unprovability in F.
> G cannot be proved in F because this requires a sequence of inference
> steps in F that prove that they themselves do not exist in F.

Right, you can't prove, in F, that G is true, but you can prove, in
Meta-F, that G is true in F, and that G is unprovable in F, which is
what is required.

You are just showing that your mind can't handle the basics of logic, or
truth.

It sounds like you are too stupid to learn, and that you have
intentionaally hamstrung yourself to avoid being "polluted" by
"rote-learning" so you are just self-inflicted ignorant.

If you won't even try to learn the basics, you have just condemned
yourself into being a pathological liar because you just don't any better.

>
> You and I can see both THAT G cannot be proved in F and WHY G cannot be
> proved in F. G cannot be proved in F for the same pathological
> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
> proved in Tarski's theory.
>

Which he didn't do, but you are too stupid to understand claissic
arguement forms.

>> Just shows you are ignorant.
>>
>> Too bad you are going to die in such disgrace.
>>
>> All you need to do is show that there exist a (possibly infinte) set
>> of steps from the truth makers in F, using the rules of F, to G. Youy
>> don't need to actually DO this in F, if you have a system that knowns
>> about F.
>>
>> Your mind is just too small.
>

On 4/22/2023 5:22 PM, Richard Damon wrote:
> On 4/22/23 6:10 PM, olcott wrote:
>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>> On 4/22/23 5:36 PM, olcott wrote:
>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>
>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>> erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>> that claim is erroneous.
>>>>>>>
>>>>>>
>>>>>> When G asserts its own unprovability in F:
>>>>>
>>>>> But Godel's G doesn't do that.
>>>>>
>>>>>>
>>>>>> Any proof of G in F requires a sequence of inference steps in F that
>>>>>> prove that they themselves do not exist in F.
>>>>>
>>>>> It is of course impossible to prove in F that a statement is true
>>>>> but not provable in F.
>>>>>
>>>>> You don't need to do the proof in F,
>>>>
>>>> To prove G in F you do.
>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>> This sentence is not true: "This sentence is not true" is true.
>>>>
>>>>
>>>
>>> So, you don't understand how to prove that something is "True in F"
>>> by doing the steps in Meta-F.
>>>
>>
>> I just showed you how Tarski proved that the Liar Paradox expressed in
>> his theory is true in his meta-theory.
>
> No, he didn't, he showed that *IF* a certain assuption was true, then
> the Liar's paradox would be true, thus that assumption can not be true.
>

When one level of indirect reference is applied to the Liar Paradox it
becomes actually true. There was no "if".

This sentence is not true: "This sentence is not true" <IS> TRUE.

> Your
>
>>
>> We can do the same thing when G asserts its own unprovability in F.
>> G cannot be proved in F because this requires a sequence of inference
>> steps in F that prove that they themselves do not exist in F.
>
> Right, you can't prove, in F, that G is true, but you can prove, in
> Meta-F, that G is true in F, and that G is unprovable in F, which is
> what is required.
>

When G asserts its own unprovability in F it cannot be proved in F
because this requires a sequence of inference steps in F that prove that
they themselves do not exist.

Meta-F merely removes the self-contradiction the same way Tarski's Meta-
theory removed the self-contradiction.

> You are just showing that your mind can't handle the basics of logic, or
> truth.
>

It may seem that way to someone that learns things by rote and mistakes
this for actual understanding of exactly how all of the elements of a
proof fit together coherently or fail to do so.

> It sounds like you are too stupid to learn, and that you have
> intentionaally hamstrung yourself to avoid being "polluted" by
> "rote-learning" so you are just self-inflicted ignorant.
>
> If you won't even try to learn the basics, you have just condemned
> yourself into being a pathological liar because you just don't any better.
>

I do at this point need to understand model theory very thoroughly.

Learning the details of these things could have boxed me into a corner
prior to my philosophical investigation of seeing how the key elements
fail to fit together coherently.

It is true that the set of analytical truth is simply a set of semantic
tautologies. It is true that formal systems grounded in this foundation
cannot be incomplete nor have any expressions of language that are
undecidable. Now that I have this foundation I have a way to see exactly
how the concepts of math diverge from correct reasoning.

>>
>> You and I can see both THAT G cannot be proved in F and WHY G cannot be
>> proved in F. G cannot be proved in F for the same pathological
>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>> proved in Tarski's theory.
>>
>
> Which he didn't do, but you are too stupid to understand claissic
> arguement forms.
>

It is not that I do not understand, it is that I can directly see where
and how formal mathematical systems diverge from correct reasoning.

Because you are a learned-by-rote person you make sure to never examine
whether or not any aspect of math diverges from correct reasoning, you
simply assume that math is the gospel even when it contradicts itself.

>>> Just shows you are ignorant.
>>>
>>> Too bad you are going to die in such disgrace.
>>>
>>> All you need to do is show that there exist a (possibly infinte) set
>>> of steps from the truth makers in F, using the rules of F, to G. Youy
>>> don't need to actually DO this in F, if you have a system that knowns
>>> about F.
>>>
>>> Your mind is just too small.
>>
>

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/23 6:49 PM, olcott wrote:
> On 4/22/2023 5:22 PM, Richard Damon wrote:
>> On 4/22/23 6:10 PM, olcott wrote:
>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>
>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>> erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>> that claim is erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> When G asserts its own unprovability in F:
>>>>>>
>>>>>> But Godel's G doesn't do that.
>>>>>>
>>>>>>>
>>>>>>> Any proof of G in F requires a sequence of inference steps in F that
>>>>>>> prove that they themselves do not exist in F.
>>>>>>
>>>>>> It is of course impossible to prove in F that a statement is true
>>>>>> but not provable in F.
>>>>>>
>>>>>> You don't need to do the proof in F,
>>>>>
>>>>> To prove G in F you do.
>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>
>>>>>
>>>>
>>>> So, you don't understand how to prove that something is "True in F"
>>>> by doing the steps in Meta-F.
>>>>
>>>
>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>> in his theory is true in his meta-theory.
>>
>> No, he didn't, he showed that *IF* a certain assuption was true, then
>> the Liar's paradox would be true, thus that assumption can not be true.
>>
>
> When one level of indirect reference is applied to the Liar Paradox it
> becomes actually true. There was no "if".
>
> This sentence is not true: "This sentence is not true" <IS> TRUE.
>
>> Your
>>
>>>
>>> We can do the same thing when G asserts its own unprovability in F.
>>> G cannot be proved in F because this requires a sequence of inference
>>> steps in F that prove that they themselves do not exist in F.
>>
>> Right, you can't prove, in F, that G is true, but you can prove, in
>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>> what is required.
>>
>
> When G asserts its own unprovability in F it cannot be proved in F
> because this requires a sequence of inference steps in F that prove that
> they themselves do not exist.
>
> Meta-F merely removes the self-contradiction the same way Tarski's Meta-
> theory removed the self-contradiction.
>
>
>> You are just showing that your mind can't handle the basics of logic,
>> or truth.
>>
>
> It may seem that way to someone that learns things by rote and mistakes
> this for actual understanding of exactly how all of the elements of a
> proof fit together coherently or fail to do so.
>
>> It sounds like you are too stupid to learn, and that you have
>> intentionaally hamstrung yourself to avoid being "polluted" by
>> "rote-learning" so you are just self-inflicted ignorant.
>>
>> If you won't even try to learn the basics, you have just condemned
>> yourself into being a pathological liar because you just don't any
>> better.
>>
>
> I do at this point need to understand model theory very thoroughly.
>
> Learning the details of these things could have boxed me into a corner
> prior to my philosophical investigation of seeing how the key elements
> fail to fit together coherently.
>
> It is true that the set of analytical truth is simply a set of semantic
> tautologies. It is true that formal systems grounded in this foundation
> cannot be incomplete nor have any expressions of language that are
> undecidable. Now that I have this foundation I have a way to see exactly
> how the concepts of math diverge from correct reasoning.
>
>>>
>>> You and I can see both THAT G cannot be proved in F and WHY G cannot be
>>> proved in F. G cannot be proved in F for the same pathological
>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>> proved in Tarski's theory.
>>>
>>
>> Which he didn't do, but you are too stupid to understand claissic
>> arguement forms.
>>
>
> It is not that I do not understand, it is that I can directly see where
> and how formal mathematical systems diverge from correct reasoning.

But since you are discussing Formal Logic, you need to use the rules of
Formal logic.

The other way to say it is that your "Correct Reasoning" diverges from
the accepted and proven system of Formal Logic.

>
> Because you are a learned-by-rote person you make sure to never examine
> whether or not any aspect of math diverges from correct reasoning, you
> simply assume that math is the gospel even when it contradicts itself.

Nope, I know that with logic, if you follow the rules, you will get the
correct answer by the rules.

If you break the rules, you have no idea where you will go.

As I have told you before, if you want to see what your "Correct
Reasoning" can do as a replaceent logic system, you need to start at the
BEGINNING, and see wht it gets.

To just try to change things at the end is just PROOF that your "Correct
Reasoning" has to not be based on any real principles of logic.

Since it is clear that you want to change some of the basics of how
logic works, you are not allowed to just use ANY of classical logic
until you actually show what part of it is still usable under your
system and what changes happen.

Considering your current status, I would start working hard on that
right away, as with your current reputation, once you go, NO ONE is
going to want to look at your ideas, because you have done such a good
job showing that you don't understand how things work.

I haven't been able to get out of you exactly what you want to do with
your "Correct Reasoning", and until you show a heart to actually try to
do something constructive with it, and not just use it as an excuse for
bad logic, I don't care what it might be able to do, because, frankly, I
don't think you have the intellect to come up with something like that.

But go ahead and prove me wrong, write an actual paper on the basics of
your "Correct Reasoning" and show how it actually works, and compare it
to "Classical Logic" and show what is different. Then maybe you can
start to work on showing it can actually do something useful.

>
>>>> Just shows you are ignorant.
>>>>
>>>> Too bad you are going to die in such disgrace.
>>>>
>>>> All you need to do is show that there exist a (possibly infinte) set
>>>> of steps from the truth makers in F, using the rules of F, to G.
>>>> Youy don't need to actually DO this in F, if you have a system that
>>>> knowns about F.
>>>>
>>>> Your mind is just too small.
>>>
>>
>

On 4/22/2023 6:19 PM, Richard Damon wrote:
> On 4/22/23 6:49 PM, olcott wrote:
>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>> On 4/22/23 6:10 PM, olcott wrote:
>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>> erroneous.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>> that claim is erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>
>>>>>>> But Godel's G doesn't do that.
>>>>>>>
>>>>>>>>
>>>>>>>> Any proof of G in F requires a sequence of inference steps in F
>>>>>>>> that
>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>
>>>>>>> It is of course impossible to prove in F that a statement is true
>>>>>>> but not provable in F.
>>>>>>>
>>>>>>> You don't need to do the proof in F,
>>>>>>
>>>>>> To prove G in F you do.
>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>
>>>>>>
>>>>>
>>>>> So, you don't understand how to prove that something is "True in F"
>>>>> by doing the steps in Meta-F.
>>>>>
>>>>
>>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>>> in his theory is true in his meta-theory.
>>>
>>> No, he didn't, he showed that *IF* a certain assuption was true, then
>>> the Liar's paradox would be true, thus that assumption can not be true.
>>>
>>
>> When one level of indirect reference is applied to the Liar Paradox it
>> becomes actually true. There was no "if".
>>
>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>
>>> Your
>>>
>>>>
>>>> We can do the same thing when G asserts its own unprovability in F.
>>>> G cannot be proved in F because this requires a sequence of inference
>>>> steps in F that prove that they themselves do not exist in F.
>>>
>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>>> what is required.
>>>
>>
>> When G asserts its own unprovability in F it cannot be proved in F
>> because this requires a sequence of inference steps in F that prove that
>> they themselves do not exist.
>>
>> Meta-F merely removes the self-contradiction the same way Tarski's Meta-
>> theory removed the self-contradiction.
>>
>>
>>> You are just showing that your mind can't handle the basics of logic,
>>> or truth.
>>>
>>
>> It may seem that way to someone that learns things by rote and mistakes
>> this for actual understanding of exactly how all of the elements of a
>> proof fit together coherently or fail to do so.
>>
>>> It sounds like you are too stupid to learn, and that you have
>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>> "rote-learning" so you are just self-inflicted ignorant.
>>>
>>> If you won't even try to learn the basics, you have just condemned
>>> yourself into being a pathological liar because you just don't any
>>> better.
>>>
>>
>> I do at this point need to understand model theory very thoroughly.
>>
>> Learning the details of these things could have boxed me into a corner
>> prior to my philosophical investigation of seeing how the key elements
>> fail to fit together coherently.
>>
>> It is true that the set of analytical truth is simply a set of semantic
>> tautologies. It is true that formal systems grounded in this foundation
>> cannot be incomplete nor have any expressions of language that are
>> undecidable. Now that I have this foundation I have a way to see exactly
>> how the concepts of math diverge from correct reasoning.
>>
>>>>
>>>> You and I can see both THAT G cannot be proved in F and WHY G cannot be
>>>> proved in F. G cannot be proved in F for the same pathological
>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>>> proved in Tarski's theory.
>>>>
>>>
>>> Which he didn't do, but you are too stupid to understand claissic
>>> arguement forms.
>>>
>>
>> It is not that I do not understand, it is that I can directly see
>> where and how formal mathematical systems diverge from correct reasoning.
>
> But since you are discussing Formal Logic, you need to use the rules of
> Formal logic.
>

I have never been talking about formal logic. I have always been talking
about the philosophical foundations of correct reasoning.

> The other way to say it is that your "Correct Reasoning" diverges from
> the accepted and proven system of Formal Logic.
>

It is correct reasoning in the absolute sense that I refer to.
If anyone has the opinion that arithmetic does not exist they are
incorrect in the absolute sense of the word: "incorrect".

>>
>> Because you are a learned-by-rote person you make sure to never examine
>> whether or not any aspect of math diverges from correct reasoning, you
>> simply assume that math is the gospel even when it contradicts itself.
>
> Nope, I know that with logic, if you follow the rules, you will get the
> correct answer by the rules.
>
> If you break the rules, you have no idea where you will go.
>

In other words you never ever spend any time on making sure that these
rules fit together coherently.

> As I have told you before, if you want to see what your "Correct > Reasoning" can do as a replaceent logic system, you need to start at the
> BEGINNING, and see wht it gets.
>

The foundation of correct reasoning is that the entire body of
analytical truth is a set of semantic tautologies.

This means that all correct inference always requires determining the
semantic consequence of expressions of language. This semantic
consequence can be specified syntactically, and indeed must be
represented syntactically to be computable.

> To just try to change things at the end is just PROOF that your "Correct
> Reasoning" has to not be based on any real principles of logic.
>
> Since it is clear that you want to change some of the basics of how
> logic works, you are not allowed to just use ANY of classical logic
> until you actually show what part of it is still usable under your
> system and what changes happen.
>

Whenever an expression of language is derived as the semantic
consequence of other expressions of language we have valid inference.

The semantic consequence must be specified syntactically so that it can
be computed or examined in formal systems.

Just like in sound deductive inference when the premises are known to be
true, and the reasoning valid (a semantic consequence) then the
conclusion is necessarily true.

> Considering your current status, I would start working hard on that
> right away, as with your current reputation, once you go, NO ONE is
> going to want to look at your ideas, because you have done such a good
> job showing that you don't understand how things work.
>

My reputation on one very important group has risen to quite credible

> I haven't been able to get out of you exactly what you want to do with
> your "Correct Reasoning", and until you show a heart to actually try to
> do something constructive with it, and not just use it as an excuse for
> bad logic, I don't care what it might be able to do, because, frankly, I
> don't think you have the intellect to come up with something like that.
>

On 4/22/23 7:57 PM, olcott wrote:
> On 4/22/2023 6:19 PM, Richard Damon wrote:
>> On 4/22/23 6:49 PM, olcott wrote:
>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>> erroneous.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>>> that claim is erroneous.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>
>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Any proof of G in F requires a sequence of inference steps in F
>>>>>>>>> that
>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>
>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>> true but not provable in F.
>>>>>>>>
>>>>>>>> You don't need to do the proof in F,
>>>>>>>
>>>>>>> To prove G in F you do.
>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> So, you don't understand how to prove that something is "True in
>>>>>> F" by doing the steps in Meta-F.
>>>>>>
>>>>>
>>>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>>>> in his theory is true in his meta-theory.
>>>>
>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>> then the Liar's paradox would be true, thus that assumption can not
>>>> be true.
>>>>
>>>
>>> When one level of indirect reference is applied to the Liar Paradox it
>>> becomes actually true. There was no "if".
>>>
>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>
>>>> Your
>>>>
>>>>>
>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>> G cannot be proved in F because this requires a sequence of inference
>>>>> steps in F that prove that they themselves do not exist in F.
>>>>
>>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>>>> what is required.
>>>>
>>>
>>> When G asserts its own unprovability in F it cannot be proved in F
>>> because this requires a sequence of inference steps in F that prove that
>>> they themselves do not exist.
>>>
>>> Meta-F merely removes the self-contradiction the same way Tarski's Meta-
>>> theory removed the self-contradiction.
>>>
>>>
>>>> You are just showing that your mind can't handle the basics of
>>>> logic, or truth.
>>>>
>>>
>>> It may seem that way to someone that learns things by rote and mistakes
>>> this for actual understanding of exactly how all of the elements of a
>>> proof fit together coherently or fail to do so.
>>>
>>>> It sounds like you are too stupid to learn, and that you have
>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>
>>>> If you won't even try to learn the basics, you have just condemned
>>>> yourself into being a pathological liar because you just don't any
>>>> better.
>>>>
>>>
>>> I do at this point need to understand model theory very thoroughly.
>>>
>>> Learning the details of these things could have boxed me into a corner
>>> prior to my philosophical investigation of seeing how the key elements
>>> fail to fit together coherently.
>>>
>>> It is true that the set of analytical truth is simply a set of semantic
>>> tautologies. It is true that formal systems grounded in this foundation
>>> cannot be incomplete nor have any expressions of language that are
>>> undecidable. Now that I have this foundation I have a way to see exactly
>>> how the concepts of math diverge from correct reasoning.
>>>
>>>>>
>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>> cannot be
>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>>>> proved in Tarski's theory.
>>>>>
>>>>
>>>> Which he didn't do, but you are too stupid to understand claissic
>>>> arguement forms.
>>>>
>>>
>>> It is not that I do not understand, it is that I can directly see
>>> where and how formal mathematical systems diverge from correct
>>> reasoning.
>>
>> But since you are discussing Formal Logic, you need to use the rules
>> of Formal logic.
>>
>
> I have never been talking about formal logic. I have always been talking
> about the philosophical foundations of correct reasoning.

No, you have been talking about theorys DEEP in formal logic. You can't
talk about the "errors" in those theories, with being in formal logic.

IF you think you can somehow talk about the foundations, while working
in the penthouse, you have just confirmed that you do not understand how
ANY form of logic works.

PERIOD.

>
>> The other way to say it is that your "Correct Reasoning" diverges from
>> the accepted and proven system of Formal Logic.
>>
>
> It is correct reasoning in the absolute sense that I refer to.
> If anyone has the opinion that arithmetic does not exist they are
> incorrect in the absolute sense of the word: "incorrect".
>

IF you reject the logic that a theory is based on, you need to reject
the logic system, NOT the theory.

You are just showing that you have wasted your LIFE because you
don'tunderstnad how to work ligic.

>>>
>>> Because you are a learned-by-rote person you make sure to never examine
>>> whether or not any aspect of math diverges from correct reasoning, you
>>> simply assume that math is the gospel even when it contradicts itself.
>>
>> Nope, I know that with logic, if you follow the rules, you will get
>> the correct answer by the rules.
>>
>> If you break the rules, you have no idea where you will go.
>>
>
> In other words you never ever spend any time on making sure that these
> rules fit together coherently.

The rules work together just fine.

YOU don't like some of the results, but they work just fine for most of
the field.

You are just PROVING that you have no idea how to actually discuss a new
foundation for logic, likely because you are incapable of actually
comeing up with a consistent basis for working logic.

>
>> As I have told you before, if you want to see what your "Correct  >
>> Reasoning" can do as a replaceent logic system, you need to start at the
>> BEGINNING, and see wht it gets.
>>
>
> The foundation of correct reasoning is that the entire body of
> analytical truth is a set of semantic tautologies.
>
> This means that all correct inference always requires determining the
> semantic consequence of expressions of language. This semantic
> consequence can be specified syntactically, and indeed must be
> represented syntactically to be computable
Meaningless gobbledy-good until you actually define what you mean and
spell out the actual rules that need to be followed.

On 4/22/2023 5:22 PM, Richard Damon wrote:
> On 4/22/23 6:10 PM, olcott wrote:
>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>> On 4/22/23 5:36 PM, olcott wrote:
>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>
>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>> erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>> that claim is erroneous.
>>>>>>>
>>>>>>
>>>>>> When G asserts its own unprovability in F:
>>>>>
>>>>> But Godel's G doesn't do that.
>>>>>
>>>>>>
>>>>>> Any proof of G in F requires a sequence of inference steps in F that
>>>>>> prove that they themselves do not exist in F.
>>>>>
>>>>> It is of course impossible to prove in F that a statement is true
>>>>> but not provable in F.
>>>>>
>>>>> You don't need to do the proof in F,
>>>>
>>>> To prove G in F you do.
>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>> This sentence is not true: "This sentence is not true" is true.
>>>>
>>>>
>>>
>>> So, you don't understand how to prove that something is "True in F"
>>> by doing the steps in Meta-F.
>>>
>>
>> I just showed you how Tarski proved that the Liar Paradox expressed in
>> his theory is true in his meta-theory.
>
> No, he didn't, he showed that *IF* a certain assuption was true, then
> the Liar's paradox would be true, thus that assumption can not be true.
>
> Your
>
>>
>> We can do the same thing when G asserts its own unprovability in F.
>> G cannot be proved in F because this requires a sequence of inference
>> steps in F that prove that they themselves do not exist in F.
>
> Right, you can't prove, in F, that G is true, but you can prove, in
> Meta-F, that G is true in F, and that G is unprovable in F, which is
> what is required.
>
> You are just showing that your mind can't handle the basics of logic, or

Proving that G is true in F requires a sequence of inference steps that
prove that they themselves don't exist.

You might be bright enough to understand that is self-contradictory.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/2023 6:19 PM, Richard Damon wrote:
> On 4/22/23 6:49 PM, olcott wrote:
>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>> On 4/22/23 6:10 PM, olcott wrote:
>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>> erroneous.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>> that claim is erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>
>>>>>>> But Godel's G doesn't do that.
>>>>>>>
>>>>>>>>
>>>>>>>> Any proof of G in F requires a sequence of inference steps in F
>>>>>>>> that
>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>
>>>>>>> It is of course impossible to prove in F that a statement is true
>>>>>>> but not provable in F.
>>>>>>>
>>>>>>> You don't need to do the proof in F,
>>>>>>
>>>>>> To prove G in F you do.
>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>
>>>>>>
>>>>>
>>>>> So, you don't understand how to prove that something is "True in F"
>>>>> by doing the steps in Meta-F.
>>>>>
>>>>
>>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>>> in his theory is true in his meta-theory.
>>>
>>> No, he didn't, he showed that *IF* a certain assuption was true, then
>>> the Liar's paradox would be true, thus that assumption can not be true.
>>>
>>
>> When one level of indirect reference is applied to the Liar Paradox it
>> becomes actually true. There was no "if".
>>
>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>
>>> Your
>>>
>>>>
>>>> We can do the same thing when G asserts its own unprovability in F.
>>>> G cannot be proved in F because this requires a sequence of inference
>>>> steps in F that prove that they themselves do not exist in F.
>>>
>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>>> what is required.
>>>
>>
>> When G asserts its own unprovability in F it cannot be proved in F
>> because this requires a sequence of inference steps in F that prove that
>> they themselves do not exist.
>>
>> Meta-F merely removes the self-contradiction the same way Tarski's Meta-
>> theory removed the self-contradiction.
>>
>>
>>> You are just showing that your mind can't handle the basics of logic,
>>> or truth.
>>>
>>
>> It may seem that way to someone that learns things by rote and mistakes
>> this for actual understanding of exactly how all of the elements of a
>> proof fit together coherently or fail to do so.
>>
>>> It sounds like you are too stupid to learn, and that you have
>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>> "rote-learning" so you are just self-inflicted ignorant.
>>>
>>> If you won't even try to learn the basics, you have just condemned
>>> yourself into being a pathological liar because you just don't any
>>> better.
>>>
>>
>> I do at this point need to understand model theory very thoroughly.
>>
>> Learning the details of these things could have boxed me into a corner
>> prior to my philosophical investigation of seeing how the key elements
>> fail to fit together coherently.
>>
>> It is true that the set of analytical truth is simply a set of semantic
>> tautologies. It is true that formal systems grounded in this foundation
>> cannot be incomplete nor have any expressions of language that are
>> undecidable. Now that I have this foundation I have a way to see exactly
>> how the concepts of math diverge from correct reasoning.
>>
>>>>
>>>> You and I can see both THAT G cannot be proved in F and WHY G cannot be
>>>> proved in F. G cannot be proved in F for the same pathological
>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>>> proved in Tarski's theory.
>>>>
>>>
>>> Which he didn't do, but you are too stupid to understand claissic
>>> arguement forms.
>>>
>>
>> It is not that I do not understand, it is that I can directly see
>> where and how formal mathematical systems diverge from correct reasoning.
>
> But since you are discussing Formal Logic, you need to use the rules of
> Formal logic.
>
> The other way to say it is that your "Correct Reasoning" diverges from
> the accepted and proven system of Formal Logic.

In classical logic, intuitionistic logic and similar logical systems,
the principle of explosion

ex falso [sequitur] quodlibet,
'from falsehood, anything [follows]'

ex contradictione [sequitur] quodlibet,
'from contradiction, anything [follows]')

https://en.wikipedia.org/wiki/Principle_of_explosion

∴ FALSE ⊢ Donald Trump is the Christ
∴ FALSE ⊢ Donald Trump is Satan

*Correction abolishing the POE nonsense*
Semantic Necessity operator: ⊨□
FALSE ⊨□ FALSE
(P ∧ ¬P) ⊨□ FALSE

>>
>> Because you are a learned-by-rote person you make sure to never examine
>> whether or not any aspect of math diverges from correct reasoning, you
>> simply assume that math is the gospel even when it contradicts itself.
>
> Nope, I know that with logic, if you follow the rules, you will get the
> correct answer by the rules.
>

Then you must agree that Trump is the Christ and Trump is Satan both of
those were derived from correct logic.

> If you break the rules, you have no idea where you will go.
>
> As I have told you before, if you want to see what your "Correct
> Reasoning" can do as a replaceent logic system, you need to start at the
> BEGINNING, and see wht it gets.
>

I would be happy to talk this through with you.

The beginning is that

valid inference an expression X of language L must be a semantic
consequence of its premises in L

sound inference expression X of language L must be a semantic
consequence of the axioms of L.

For formal systems such as FOL the semantics is mostly the meaning of
the logic symbols.

These two logic symbols are abolished ⇒ → and replaced with this:
Semantic Necessity operator: ⊨□

> To just try to change things at the end is just PROOF that your "Correct
> Reasoning" has to not be based on any real principles of logic.
>

No logic must be based on correct reasoning any logic that prove Donal
Trump is the Christ is incorrect reasoning, thus the POE is abolished

These two logic symbols are abolished ⇒ → and replaced with this:
Semantic Necessity operator: ⊨□

Explosions have been abolished
FALSE ⊨□ FALSE
(P ∧ ¬P) ⊨□ FALSE

> Since it is clear that you want to change some of the basics of how
> logic works, you are not allowed to just use ANY of classical logic
> until you actually show what part of it is still usable under your
> system and what changes happen.
>

Yes lets apply my ideas to FOL. I have already sketched out many
details.

> Considering your current status, I would start working hard on that
> right away, as with your current reputation, once you go, NO ONE is
> going to want to look at your ideas, because you have done such a good
> job showing that you don't understand how things work.
>
> I haven't been able to get out of you exactly what you want to do with
> your "Correct Reasoning", and until you show a heart to actually try to
> do something constructive with it, and not just use it as an excuse for
> bad logic, I don't care what it might be able to do, because, frankly, I
> don't think you have the intellect to come up with something like that.
>

On 4/22/2023 7:27 PM, Richard Damon wrote:
> On 4/22/23 7:57 PM, olcott wrote:
>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>> On 4/22/23 6:49 PM, olcott wrote:
>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>
>>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>>> erroneous.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>>>> that claim is erroneous.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>
>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Any proof of G in F requires a sequence of inference steps in
>>>>>>>>>> F that
>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>
>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>> true but not provable in F.
>>>>>>>>>
>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>
>>>>>>>> To prove G in F you do.
>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> So, you don't understand how to prove that something is "True in
>>>>>>> F" by doing the steps in Meta-F.
>>>>>>>
>>>>>>
>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>> expressed in his theory is true in his meta-theory.
>>>>>
>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>> then the Liar's paradox would be true, thus that assumption can not
>>>>> be true.
>>>>>
>>>>
>>>> When one level of indirect reference is applied to the Liar Paradox it
>>>> becomes actually true. There was no "if".
>>>>
>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>
>>>>> Your
>>>>>
>>>>>>
>>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>>> G cannot be proved in F because this requires a sequence of inference
>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>
>>>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>>>> Meta-F, that G is true in F, and that G is unprovable in F, which
>>>>> is what is required.
>>>>>
>>>>
>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>> because this requires a sequence of inference steps in F that prove
>>>> that
>>>> they themselves do not exist.
>>>>
>>>> Meta-F merely removes the self-contradiction the same way Tarski's
>>>> Meta-
>>>> theory removed the self-contradiction.
>>>>
>>>>
>>>>> You are just showing that your mind can't handle the basics of
>>>>> logic, or truth.
>>>>>
>>>>
>>>> It may seem that way to someone that learns things by rote and mistakes
>>>> this for actual understanding of exactly how all of the elements of a
>>>> proof fit together coherently or fail to do so.
>>>>
>>>>> It sounds like you are too stupid to learn, and that you have
>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>
>>>>> If you won't even try to learn the basics, you have just condemned
>>>>> yourself into being a pathological liar because you just don't any
>>>>> better.
>>>>>
>>>>
>>>> I do at this point need to understand model theory very thoroughly.
>>>>
>>>> Learning the details of these things could have boxed me into a corner
>>>> prior to my philosophical investigation of seeing how the key elements
>>>> fail to fit together coherently.
>>>>
>>>> It is true that the set of analytical truth is simply a set of semantic
>>>> tautologies. It is true that formal systems grounded in this foundation
>>>> cannot be incomplete nor have any expressions of language that are
>>>> undecidable. Now that I have this foundation I have a way to see
>>>> exactly
>>>> how the concepts of math diverge from correct reasoning.
>>>>
>>>>>>
>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>> cannot be
>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>>>>> proved in Tarski's theory.
>>>>>>
>>>>>
>>>>> Which he didn't do, but you are too stupid to understand claissic
>>>>> arguement forms.
>>>>>
>>>>
>>>> It is not that I do not understand, it is that I can directly see
>>>> where and how formal mathematical systems diverge from correct
>>>> reasoning.
>>>
>>> But since you are discussing Formal Logic, you need to use the rules
>>> of Formal logic.
>>>
>>
>> I have never been talking about formal logic. I have always been talking
>> about the philosophical foundations of correct reasoning.
>
> No, you have been talking about theorys DEEP in formal logic. You can't
> talk about the "errors" in those theories, with being in formal logic.
>
> IF you think you can somehow talk about the foundations, while working
> in the penthouse, you have just confirmed that you do not understand how
> ANY form of logic works.
>
> PERIOD.
>
>
>>
>>> The other way to say it is that your "Correct Reasoning" diverges
>>> from the accepted and proven system of Formal Logic.
>>>
>>
>> It is correct reasoning in the absolute sense that I refer to.
>> If anyone has the opinion that arithmetic does not exist they are
>> incorrect in the absolute sense of the word: "incorrect".
>>
>
> IF you reject the logic that a theory is based on, you need to reject
> the logic system, NOT the theory.
>
> You are just showing that you have wasted your LIFE because you
> don'tunderstnad how to work ligic.
>
>>>>
>>>> Because you are a learned-by-rote person you make sure to never examine
>>>> whether or not any aspect of math diverges from correct reasoning, you
>>>> simply assume that math is the gospel even when it contradicts itself.
>>>
>>> Nope, I know that with logic, if you follow the rules, you will get
>>> the correct answer by the rules.
>>>
>>> If you break the rules, you have no idea where you will go.
>>>
>>
>> In other words you never ever spend any time on making sure that these
>> rules fit together coherently.
>
> The rules work together just fine.
>
> YOU don't like some of the results, but they work just fine for most of
> the field.
>
> You are just PROVING that you have no idea how to actually discuss a new
> foundation for logic, likely because you are incapable of actually
> comeing up with a consistent basis for working logic.
>
>>
>>> As I have told you before, if you want to see what your "Correct  >
>>> Reasoning" can do as a replaceent logic system, you need to start at the
>>> BEGINNING, and see wht it gets.
>>>
>>
>> The foundation of correct reasoning is that the entire body of
>> analytical truth is a set of semantic tautologies.
>>
>> This means that all correct inference always requires determining the
>> semantic consequence of expressions of language. This semantic
>> consequence can be specified syntactically, and indeed must be
>> represented syntactically to be computable
> Meaningless gobbledy-good until you actually define what you mean and
> spell out the actual rules that need to be followed.
>
> Note, "Computability" is actually a fairly late in the process concept.
> You first need to show that you logic can actually do something useful
>
>>
>>> To just try to change things at the end is just PROOF that your
>>> "Correct Reasoning" has to not be based on any real principles of logic.
>>>
>>> Since it is clear that you want to change some of the basics of how
>>> logic works, you are not allowed to just use ANY of classical logic
>>> until you actually show what part of it is still usable under your
>>> system and what changes happen.
>>>
>>
>> Whenever an expression of language is derived as the semantic
>> consequence of other expressions of language we have valid inference.
>
> And, are you using the "classical" definition of "semantic" (which makes
> this sentence somewhat cirular) or do you mean something based on the
> concept you sometimes use of  "the meaning of the words".
>

On 4/24/2023 10:58 AM, olcott wrote:
> On 4/22/2023 7:27 PM, Richard Damon wrote:
>> On 4/22/23 7:57 PM, olcott wrote:
>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>>>> erroneous.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>
>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps in
>>>>>>>>>>> F that
>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>
>>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>>> true but not provable in F.
>>>>>>>>>>
>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>
>>>>>>>>> To prove G in F you do.
>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> So, you don't understand how to prove that something is "True in
>>>>>>>> F" by doing the steps in Meta-F.
>>>>>>>>
>>>>>>>
>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>
>>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>>> then the Liar's paradox would be true, thus that assumption can
>>>>>> not be true.
>>>>>>
>>>>>
>>>>> When one level of indirect reference is applied to the Liar Paradox it
>>>>> becomes actually true. There was no "if".
>>>>>
>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>
>>>>>> Your
>>>>>>
>>>>>>>
>>>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>> inference
>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>
>>>>>> Right, you can't prove, in F, that G is true, but you can prove,
>>>>>> in Meta-F, that G is true in F, and that G is unprovable in F,
>>>>>> which is what is required.
>>>>>>
>>>>>
>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>> because this requires a sequence of inference steps in F that prove
>>>>> that
>>>>> they themselves do not exist.
>>>>>
>>>>> Meta-F merely removes the self-contradiction the same way Tarski's
>>>>> Meta-
>>>>> theory removed the self-contradiction.
>>>>>
>>>>>
>>>>>> You are just showing that your mind can't handle the basics of
>>>>>> logic, or truth.
>>>>>>
>>>>>
>>>>> It may seem that way to someone that learns things by rote and
>>>>> mistakes
>>>>> this for actual understanding of exactly how all of the elements of a
>>>>> proof fit together coherently or fail to do so.
>>>>>
>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>
>>>>>> If you won't even try to learn the basics, you have just condemned
>>>>>> yourself into being a pathological liar because you just don't any
>>>>>> better.
>>>>>>
>>>>>
>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>
>>>>> Learning the details of these things could have boxed me into a corner
>>>>> prior to my philosophical investigation of seeing how the key elements
>>>>> fail to fit together coherently.
>>>>>
>>>>> It is true that the set of analytical truth is simply a set of
>>>>> semantic
>>>>> tautologies. It is true that formal systems grounded in this
>>>>> foundation
>>>>> cannot be incomplete nor have any expressions of language that are
>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>> exactly
>>>>> how the concepts of math diverge from correct reasoning.
>>>>>
>>>>>>>
>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>> cannot be
>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot
>>>>>>> be proved in Tarski's theory.
>>>>>>>
>>>>>>
>>>>>> Which he didn't do, but you are too stupid to understand claissic
>>>>>> arguement forms.
>>>>>>
>>>>>
>>>>> It is not that I do not understand, it is that I can directly see
>>>>> where and how formal mathematical systems diverge from correct
>>>>> reasoning.
>>>>
>>>> But since you are discussing Formal Logic, you need to use the rules
>>>> of Formal logic.
>>>>
>>>
>>> I have never been talking about formal logic. I have always been talking
>>> about the philosophical foundations of correct reasoning.
>>
>> No, you have been talking about theorys DEEP in formal logic. You
>> can't talk about the "errors" in those theories, with being in formal
>> logic.
>>
>> IF you think you can somehow talk about the foundations, while working
>> in the penthouse, you have just confirmed that you do not understand
>> how ANY form of logic works.
>>
>> PERIOD.
>>
>>
>>>
>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>> from the accepted and proven system of Formal Logic.
>>>>
>>>
>>> It is correct reasoning in the absolute sense that I refer to.
>>> If anyone has the opinion that arithmetic does not exist they are
>>> incorrect in the absolute sense of the word: "incorrect".
>>>
>>
>> IF you reject the logic that a theory is based on, you need to reject
>> the logic system, NOT the theory.
>>
>> You are just showing that you have wasted your LIFE because you
>> don'tunderstnad how to work ligic.
>>
>>>>>
>>>>> Because you are a learned-by-rote person you make sure to never
>>>>> examine
>>>>> whether or not any aspect of math diverges from correct reasoning, you
>>>>> simply assume that math is the gospel even when it contradicts itself.
>>>>
>>>> Nope, I know that with logic, if you follow the rules, you will get
>>>> the correct answer by the rules.
>>>>
>>>> If you break the rules, you have no idea where you will go.
>>>>
>>>
>>> In other words you never ever spend any time on making sure that these
>>> rules fit together coherently.
>>
>> The rules work together just fine.
>>
>> YOU don't like some of the results, but they work just fine for most
>> of the field.
>>
>> You are just PROVING that you have no idea how to actually discuss a
>> new foundation for logic, likely because you are incapable of actually
>> comeing up with a consistent basis for working logic.
>>
>>>
>>>> As I have told you before, if you want to see what your "Correct  >
>>>> Reasoning" can do as a replaceent logic system, you need to start at
>>>> the
>>>> BEGINNING, and see wht it gets.
>>>>
>>>
>>> The foundation of correct reasoning is that the entire body of
>>> analytical truth is a set of semantic tautologies.
>>>
>>> This means that all correct inference always requires determining the
>>> semantic consequence of expressions of language. This semantic
>>> consequence can be specified syntactically, and indeed must be
>>> represented syntactically to be computable
>> Meaningless gobbledy-good until you actually define what you mean and
>> spell out the actual rules that need to be followed.
>>
>> Note, "Computability" is actually a fairly late in the process
>> concept. You first need to show that you logic can actually do
>> something useful
>>
>>>
>>>> To just try to change things at the end is just PROOF that your
>>>> "Correct Reasoning" has to not be based on any real principles of
>>>> logic.
>>>>
>>>> Since it is clear that you want to change some of the basics of how
>>>> logic works, you are not allowed to just use ANY of classical logic
>>>> until you actually show what part of it is still usable under your
>>>> system and what changes happen.
>>>>
>>>
>>> Whenever an expression of language is derived as the semantic
>>> consequence of other expressions of language we have valid inference.
>>
>> And, are you using the "classical" definition of "semantic" (which
>> makes this sentence somewhat cirular) or do you mean something based
>> on the concept you sometimes use of  "the meaning of the words".
>>
>
> *Principle of explosion*
> An alternate argument for the principle stems from model theory. A
> sentence P is a semantic consequence of a set of sentences Γ only if
> every model of Γ is a model of P. However, there is no model of the
> contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
> that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P) is a
> model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
> https://en.wikipedia.org/wiki/Principle_of_explosion
>
> Vacuous truth does not count as truth.
> All variables must be quantified
>
> "all cell phones in the room are turned off" will be true when no cell
> phones are in the room.
>
> ∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))
>
>
>>>
>>> The semantic consequence must be specified syntactically so that it can
>>> be computed or examined in formal systems.
>>>
>>> Just like in sound deductive inference when the premises are known to be
>>> true, and the reasoning valid (a semantic consequence) then the
>>> conclusion is necessarily true.
>>
>> So, what is the difference in your system from classical Formal Logic?
>>
>
> Semantic Necessity operator: ⊨□
>
>    FALSE ⊨□ FALSE // POE abolished
> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>
> ⇒ and → symbols are replaced by ⊨□
>
> The sets that the variables range over must be defined
> all variables must be quantified
>
> // x is a semantic consequence of its premises in L
> Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)
>
> // x is a semantic consequence of the axioms of L
> True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)
>
> *The above is all that I know right now*
>
>
>>> The most important aspect of the tiny little foundation of a formal
>>> system that I already specified immediately above is self-evident:
>>> True(L,X) can be defined and incompleteness is impossible.
>>
>> I don't think your system is anywhere near establish far enough for
>> you to say that.
>
> Try and show exceptions to this rule and I will fill in any gaps that
> you find.
>
> G asserts its own unprovability in F
> The reason that G cannot be proved in F is that this requires a
> sequence of inference steps in F that proves no such sequence
> of inference steps exists in F.
>
>
∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
∄sequence_of_inference_steps ⊆ F)

On 4/24/23 12:13 PM, olcott wrote:
> On 4/24/2023 10:58 AM, olcott wrote:
>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>>> On 4/22/23 7:57 PM, olcott wrote:
>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making
>>>>>>>>>>>>>> it erroneous.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>
>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps
>>>>>>>>>>>> in F that
>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>
>>>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>>>> true but not provable in F.
>>>>>>>>>>>
>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>
>>>>>>>>>> To prove G in F you do.
>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So, you don't understand how to prove that something is "True
>>>>>>>>> in F" by doing the steps in Meta-F.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>
>>>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>>>> then the Liar's paradox would be true, thus that assumption can
>>>>>>> not be true.
>>>>>>>
>>>>>>
>>>>>> When one level of indirect reference is applied to the Liar
>>>>>> Paradox it
>>>>>> becomes actually true. There was no "if".
>>>>>>
>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>
>>>>>>> Your
>>>>>>>
>>>>>>>>
>>>>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>> inference
>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>
>>>>>>> Right, you can't prove, in F, that G is true, but you can prove,
>>>>>>> in Meta-F, that G is true in F, and that G is unprovable in F,
>>>>>>> which is what is required.
>>>>>>>
>>>>>>
>>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>>> because this requires a sequence of inference steps in F that
>>>>>> prove that
>>>>>> they themselves do not exist.
>>>>>>
>>>>>> Meta-F merely removes the self-contradiction the same way Tarski's
>>>>>> Meta-
>>>>>> theory removed the self-contradiction.
>>>>>>
>>>>>>
>>>>>>> You are just showing that your mind can't handle the basics of
>>>>>>> logic, or truth.
>>>>>>>
>>>>>>
>>>>>> It may seem that way to someone that learns things by rote and
>>>>>> mistakes
>>>>>> this for actual understanding of exactly how all of the elements of a
>>>>>> proof fit together coherently or fail to do so.
>>>>>>
>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>
>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>> just don't any better.
>>>>>>>
>>>>>>
>>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>>
>>>>>> Learning the details of these things could have boxed me into a
>>>>>> corner
>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>> elements
>>>>>> fail to fit together coherently.
>>>>>>
>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>> semantic
>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>> foundation
>>>>>> cannot be incomplete nor have any expressions of language that are
>>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>>> exactly
>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>
>>>>>>>>
>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>>> cannot be
>>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot
>>>>>>>> be proved in Tarski's theory.
>>>>>>>>
>>>>>>>
>>>>>>> Which he didn't do, but you are too stupid to understand claissic
>>>>>>> arguement forms.
>>>>>>>
>>>>>>
>>>>>> It is not that I do not understand, it is that I can directly see
>>>>>> where and how formal mathematical systems diverge from correct
>>>>>> reasoning.
>>>>>
>>>>> But since you are discussing Formal Logic, you need to use the
>>>>> rules of Formal logic.
>>>>>
>>>>
>>>> I have never been talking about formal logic. I have always been
>>>> talking
>>>> about the philosophical foundations of correct reasoning.
>>>
>>> No, you have been talking about theorys DEEP in formal logic. You
>>> can't talk about the "errors" in those theories, with being in formal
>>> logic.
>>>
>>> IF you think you can somehow talk about the foundations, while
>>> working in the penthouse, you have just confirmed that you do not
>>> understand how ANY form of logic works.
>>>
>>> PERIOD.
>>>
>>>
>>>>
>>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>>> from the accepted and proven system of Formal Logic.
>>>>>
>>>>
>>>> It is correct reasoning in the absolute sense that I refer to.
>>>> If anyone has the opinion that arithmetic does not exist they are
>>>> incorrect in the absolute sense of the word: "incorrect".
>>>>
>>>
>>> IF you reject the logic that a theory is based on, you need to reject
>>> the logic system, NOT the theory.
>>>
>>> You are just showing that you have wasted your LIFE because you
>>> don'tunderstnad how to work ligic.
>>>
>>>>>>
>>>>>> Because you are a learned-by-rote person you make sure to never
>>>>>> examine
>>>>>> whether or not any aspect of math diverges from correct reasoning,
>>>>>> you
>>>>>> simply assume that math is the gospel even when it contradicts
>>>>>> itself.
>>>>>
>>>>> Nope, I know that with logic, if you follow the rules, you will get
>>>>> the correct answer by the rules.
>>>>>
>>>>> If you break the rules, you have no idea where you will go.
>>>>>
>>>>
>>>> In other words you never ever spend any time on making sure that these
>>>> rules fit together coherently.
>>>
>>> The rules work together just fine.
>>>
>>> YOU don't like some of the results, but they work just fine for most
>>> of the field.
>>>
>>> You are just PROVING that you have no idea how to actually discuss a
>>> new foundation for logic, likely because you are incapable of
>>> actually comeing up with a consistent basis for working logic.
>>>
>>>>
>>>>> As I have told you before, if you want to see what your "Correct  >
>>>>> Reasoning" can do as a replaceent logic system, you need to start
>>>>> at the
>>>>> BEGINNING, and see wht it gets.
>>>>>
>>>>
>>>> The foundation of correct reasoning is that the entire body of
>>>> analytical truth is a set of semantic tautologies.
>>>>
>>>> This means that all correct inference always requires determining the
>>>> semantic consequence of expressions of language. This semantic
>>>> consequence can be specified syntactically, and indeed must be
>>>> represented syntactically to be computable
>>> Meaningless gobbledy-good until you actually define what you mean and
>>> spell out the actual rules that need to be followed.
>>>
>>> Note, "Computability" is actually a fairly late in the process
>>> concept. You first need to show that you logic can actually do
>>> something useful
>>>
>>>>
>>>>> To just try to change things at the end is just PROOF that your
>>>>> "Correct Reasoning" has to not be based on any real principles of
>>>>> logic.
>>>>>
>>>>> Since it is clear that you want to change some of the basics of how
>>>>> logic works, you are not allowed to just use ANY of classical logic
>>>>> until you actually show what part of it is still usable under your
>>>>> system and what changes happen.
>>>>>
>>>>
>>>> Whenever an expression of language is derived as the semantic
>>>> consequence of other expressions of language we have valid inference.
>>>
>>> And, are you using the "classical" definition of "semantic" (which
>>> makes this sentence somewhat cirular) or do you mean something based
>>> on the concept you sometimes use of  "the meaning of the words".
>>>
>>
>> *Principle of explosion*
>> An alternate argument for the principle stems from model theory. A
>> sentence P is a semantic consequence of a set of sentences Γ only if
>> every model of Γ is a model of P. However, there is no model of the
>> contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
>> that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P) is a
>> model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> Vacuous truth does not count as truth.
>> All variables must be quantified
>>
>> "all cell phones in the room are turned off" will be true when no cell
>> phones are in the room.
>>
>> ∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))
>>
>>
>>>>
>>>> The semantic consequence must be specified syntactically so that it can
>>>> be computed or examined in formal systems.
>>>>
>>>> Just like in sound deductive inference when the premises are known
>>>> to be
>>>> true, and the reasoning valid (a semantic consequence) then the
>>>> conclusion is necessarily true.
>>>
>>> So, what is the difference in your system from classical Formal Logic?
>>>
>>
>> Semantic Necessity operator: ⊨□
>>
>>     FALSE ⊨□ FALSE // POE abolished
>> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>>
>> ⇒ and → symbols are replaced by ⊨□
>>
>> The sets that the variables range over must be defined
>> all variables must be quantified
>>
>> // x is a semantic consequence of its premises in L
>> Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)
>>
>> // x is a semantic consequence of the axioms of L
>> True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)
>>
>> *The above is all that I know right now*
>>
>>
>>>> The most important aspect of the tiny little foundation of a formal
>>>> system that I already specified immediately above is self-evident:
>>>> True(L,X) can be defined and incompleteness is impossible.
>>>
>>> I don't think your system is anywhere near establish far enough for
>>> you to say that.
>>
>> Try and show exceptions to this rule and I will fill in any gaps that
>> you find.
>>
>> G asserts its own unprovability in F
>> The reason that G cannot be proved in F is that this requires a
>> sequence of inference steps in F that proves no such sequence
>> of inference steps exists in F.
>>
>>
> ∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
> ∄sequence_of_inference_steps ⊆ F)
>
>

On 4/24/23 11:25 AM, olcott wrote:
> On 4/22/2023 6:19 PM, Richard Damon wrote:
>> On 4/22/23 6:49 PM, olcott wrote:
>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>> erroneous.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>>> that claim is erroneous.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>
>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Any proof of G in F requires a sequence of inference steps in F
>>>>>>>>> that
>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>
>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>> true but not provable in F.
>>>>>>>>
>>>>>>>> You don't need to do the proof in F,
>>>>>>>
>>>>>>> To prove G in F you do.
>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> So, you don't understand how to prove that something is "True in
>>>>>> F" by doing the steps in Meta-F.
>>>>>>
>>>>>
>>>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>>>> in his theory is true in his meta-theory.
>>>>
>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>> then the Liar's paradox would be true, thus that assumption can not
>>>> be true.
>>>>
>>>
>>> When one level of indirect reference is applied to the Liar Paradox it
>>> becomes actually true. There was no "if".
>>>
>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>
>>>> Your
>>>>
>>>>>
>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>> G cannot be proved in F because this requires a sequence of inference
>>>>> steps in F that prove that they themselves do not exist in F.
>>>>
>>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>>>> what is required.
>>>>
>>>
>>> When G asserts its own unprovability in F it cannot be proved in F
>>> because this requires a sequence of inference steps in F that prove that
>>> they themselves do not exist.
>>>
>>> Meta-F merely removes the self-contradiction the same way Tarski's Meta-
>>> theory removed the self-contradiction.
>>>
>>>
>>>> You are just showing that your mind can't handle the basics of
>>>> logic, or truth.
>>>>
>>>
>>> It may seem that way to someone that learns things by rote and mistakes
>>> this for actual understanding of exactly how all of the elements of a
>>> proof fit together coherently or fail to do so.
>>>
>>>> It sounds like you are too stupid to learn, and that you have
>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>
>>>> If you won't even try to learn the basics, you have just condemned
>>>> yourself into being a pathological liar because you just don't any
>>>> better.
>>>>
>>>
>>> I do at this point need to understand model theory very thoroughly.
>>>
>>> Learning the details of these things could have boxed me into a corner
>>> prior to my philosophical investigation of seeing how the key elements
>>> fail to fit together coherently.
>>>
>>> It is true that the set of analytical truth is simply a set of semantic
>>> tautologies. It is true that formal systems grounded in this foundation
>>> cannot be incomplete nor have any expressions of language that are
>>> undecidable. Now that I have this foundation I have a way to see exactly
>>> how the concepts of math diverge from correct reasoning.
>>>
>>>>>
>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>> cannot be
>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>>>> proved in Tarski's theory.
>>>>>
>>>>
>>>> Which he didn't do, but you are too stupid to understand claissic
>>>> arguement forms.
>>>>
>>>
>>> It is not that I do not understand, it is that I can directly see
>>> where and how formal mathematical systems diverge from correct
>>> reasoning.
>>
>> But since you are discussing Formal Logic, you need to use the rules
>> of Formal logic.
>>
>> The other way to say it is that your "Correct Reasoning" diverges from
>> the accepted and proven system of Formal Logic.
>
>
>
> In classical logic, intuitionistic logic and similar logical systems,
> the principle of explosion
>
> ex falso [sequitur] quodlibet,
> 'from falsehood, anything [follows]'
>
> ex contradictione [sequitur] quodlibet,
> 'from contradiction, anything [follows]')

Right, if a logic system can prove a contradiction, that out of that
contradiction you can prove anything

>
> https://en.wikipedia.org/wiki/Principle_of_explosion
>
> ∴ FALSE ⊢ Donald Trump is the Christ
> ∴ FALSE ⊢ Donald Trump is Satan

Which isn't what was being talked about.

You clearly don't understand how the principle of explosion works, which
isn't surprising considering how many misconseptions you have about how
logic works.

Right now, I would say you are to ignorant on that basics of logic to be
able to explain, even in basic terms, how it works, you have shown
yourself to be that stupid.

>
> *Correction abolishing the POE nonsense*
> Semantic Necessity operator: ⊨□
> FALSE ⊨□ FALSE
> (P ∧ ¬P) ⊨□ FALSE
>

So, FULLY define what you mean by that.

>
>>>
>>> Because you are a learned-by-rote person you make sure to never examine
>>> whether or not any aspect of math diverges from correct reasoning, you
>>> simply assume that math is the gospel even when it contradicts itself.
>>
>> Nope, I know that with logic, if you follow the rules, you will get
>> the correct answer by the rules.
>>
>
> Then you must agree that Trump is the Christ and Trump is Satan both of
> those were derived from correct logic.
>
>> If you break the rules, you have no idea where you will go.
>>
>> As I have told you before, if you want to see what your "Correct
>> Reasoning" can do as a replaceent logic system, you need to start at
>> the BEGINNING, and see wht it gets.
>>
>
> I would be happy to talk this through with you.
>
> The beginning is that
>
> valid inference an expression X of language L must be a semantic
> consequence of its premises in L

And what do you mean by "semantic"

On 4/24/23 10:40 AM, olcott wrote:
> On 4/22/2023 5:22 PM, Richard Damon wrote:
>> On 4/22/23 6:10 PM, olcott wrote:
>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>
>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>> erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>> that claim is erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> When G asserts its own unprovability in F:
>>>>>>
>>>>>> But Godel's G doesn't do that.
>>>>>>
>>>>>>>
>>>>>>> Any proof of G in F requires a sequence of inference steps in F that
>>>>>>> prove that they themselves do not exist in F.
>>>>>>
>>>>>> It is of course impossible to prove in F that a statement is true
>>>>>> but not provable in F.
>>>>>>
>>>>>> You don't need to do the proof in F,
>>>>>
>>>>> To prove G in F you do.
>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>
>>>>>
>>>>
>>>> So, you don't understand how to prove that something is "True in F"
>>>> by doing the steps in Meta-F.
>>>>
>>>
>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>> in his theory is true in his meta-theory.
>>
>> No, he didn't, he showed that *IF* a certain assuption was true, then
>> the Liar's paradox would be true, thus that assumption can not be true.
>>
>> Your
>>
>>>
>>> We can do the same thing when G asserts its own unprovability in F.
>>> G cannot be proved in F because this requires a sequence of inference
>>> steps in F that prove that they themselves do not exist in F.
>>
>> Right, you can't prove, in F, that G is true, but you can prove, in
>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>> what is required.
>>
>> You are just showing that your mind can't handle the basics of logic, or
>
> Proving that G is true in F requires a sequence of inference steps that
> prove that they themselves don't exist.
>
> You might be bright enough to understand that is self-contradictory.
>

Except that G is proved in Meta-F to be "True in F".

With a finite number of steps in Meta-F, we can prove that the infinite
number of steps in F exist and are true.

In particular, in F, we need to check every number individual to see if
it satisfies the relationship, and we have no short cut to make this
operation finite, so we can't prove it. But in Meta-F, we know something
about the relationship, and are able to prove that no number can satisfy
the relationship, and do so in a finite number of steps.

Thus, we can prove in Meta-F that G must be true in F.

The sequence of steps in F is infinite, so not a proof in F.

In fact, in Meta-F we are also able to prove that there CAN'T be a
finite sequence set of steps that prove G true in F.

Thus, with logic in Meta-F, we can prove that, G is True in F and can
not be proven in F.

You just don't seem to understand how Meta-Logic works. And, it turns
out, that meta-logic is a very important tool for proving things, so
this is one of your Kryponites.

On 4/24/2023 6:35 PM, Richard Damon wrote:
> On 4/24/23 12:13 PM, olcott wrote:
>> On 4/24/2023 10:58 AM, olcott wrote:
>>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>>>> On 4/22/23 7:57 PM, olcott wrote:
>>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making
>>>>>>>>>>>>>>> it erroneous.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>>
>>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps
>>>>>>>>>>>>> in F that
>>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>>
>>>>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>>>>> true but not provable in F.
>>>>>>>>>>>>
>>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>>
>>>>>>>>>>> To prove G in F you do.
>>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, you don't understand how to prove that something is "True
>>>>>>>>>> in F" by doing the steps in Meta-F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>>
>>>>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>>>>> then the Liar's paradox would be true, thus that assumption can
>>>>>>>> not be true.
>>>>>>>>
>>>>>>>
>>>>>>> When one level of indirect reference is applied to the Liar
>>>>>>> Paradox it
>>>>>>> becomes actually true. There was no "if".
>>>>>>>
>>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>>
>>>>>>>> Your
>>>>>>>>
>>>>>>>>>
>>>>>>>>> We can do the same thing when G asserts its own unprovability
>>>>>>>>> in F.
>>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>>> inference
>>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>>
>>>>>>>> Right, you can't prove, in F, that G is true, but you can prove,
>>>>>>>> in Meta-F, that G is true in F, and that G is unprovable in F,
>>>>>>>> which is what is required.
>>>>>>>>
>>>>>>>
>>>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>>>> because this requires a sequence of inference steps in F that
>>>>>>> prove that
>>>>>>> they themselves do not exist.
>>>>>>>
>>>>>>> Meta-F merely removes the self-contradiction the same way
>>>>>>> Tarski's Meta-
>>>>>>> theory removed the self-contradiction.
>>>>>>>
>>>>>>>
>>>>>>>> You are just showing that your mind can't handle the basics of
>>>>>>>> logic, or truth.
>>>>>>>>
>>>>>>>
>>>>>>> It may seem that way to someone that learns things by rote and
>>>>>>> mistakes
>>>>>>> this for actual understanding of exactly how all of the elements
>>>>>>> of a
>>>>>>> proof fit together coherently or fail to do so.
>>>>>>>
>>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>>
>>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>>> just don't any better.
>>>>>>>>
>>>>>>>
>>>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>>>
>>>>>>> Learning the details of these things could have boxed me into a
>>>>>>> corner
>>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>>> elements
>>>>>>> fail to fit together coherently.
>>>>>>>
>>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>>> semantic
>>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>>> foundation
>>>>>>> cannot be incomplete nor have any expressions of language that are
>>>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>>>> exactly
>>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>>
>>>>>>>>>
>>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>>>> cannot be
>>>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot
>>>>>>>>> be proved in Tarski's theory.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Which he didn't do, but you are too stupid to understand
>>>>>>>> claissic arguement forms.
>>>>>>>>
>>>>>>>
>>>>>>> It is not that I do not understand, it is that I can directly see
>>>>>>> where and how formal mathematical systems diverge from correct
>>>>>>> reasoning.
>>>>>>
>>>>>> But since you are discussing Formal Logic, you need to use the
>>>>>> rules of Formal logic.
>>>>>>
>>>>>
>>>>> I have never been talking about formal logic. I have always been
>>>>> talking
>>>>> about the philosophical foundations of correct reasoning.
>>>>
>>>> No, you have been talking about theorys DEEP in formal logic. You
>>>> can't talk about the "errors" in those theories, with being in
>>>> formal logic.
>>>>
>>>> IF you think you can somehow talk about the foundations, while
>>>> working in the penthouse, you have just confirmed that you do not
>>>> understand how ANY form of logic works.
>>>>
>>>> PERIOD.
>>>>
>>>>
>>>>>
>>>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>>>> from the accepted and proven system of Formal Logic.
>>>>>>
>>>>>
>>>>> It is correct reasoning in the absolute sense that I refer to.
>>>>> If anyone has the opinion that arithmetic does not exist they are
>>>>> incorrect in the absolute sense of the word: "incorrect".
>>>>>
>>>>
>>>> IF you reject the logic that a theory is based on, you need to
>>>> reject the logic system, NOT the theory.
>>>>
>>>> You are just showing that you have wasted your LIFE because you
>>>> don'tunderstnad how to work ligic.
>>>>
>>>>>>>
>>>>>>> Because you are a learned-by-rote person you make sure to never
>>>>>>> examine
>>>>>>> whether or not any aspect of math diverges from correct
>>>>>>> reasoning, you
>>>>>>> simply assume that math is the gospel even when it contradicts
>>>>>>> itself.
>>>>>>
>>>>>> Nope, I know that with logic, if you follow the rules, you will
>>>>>> get the correct answer by the rules.
>>>>>>
>>>>>> If you break the rules, you have no idea where you will go.
>>>>>>
>>>>>
>>>>> In other words you never ever spend any time on making sure that these
>>>>> rules fit together coherently.
>>>>
>>>> The rules work together just fine.
>>>>
>>>> YOU don't like some of the results, but they work just fine for most
>>>> of the field.
>>>>
>>>> You are just PROVING that you have no idea how to actually discuss a
>>>> new foundation for logic, likely because you are incapable of
>>>> actually comeing up with a consistent basis for working logic.
>>>>
>>>>>
>>>>>> As I have told you before, if you want to see what your "Correct
>>>>>> > Reasoning" can do as a replaceent logic system, you need to
>>>>>> start at the
>>>>>> BEGINNING, and see wht it gets.
>>>>>>
>>>>>
>>>>> The foundation of correct reasoning is that the entire body of
>>>>> analytical truth is a set of semantic tautologies.
>>>>>
>>>>> This means that all correct inference always requires determining the
>>>>> semantic consequence of expressions of language. This semantic
>>>>> consequence can be specified syntactically, and indeed must be
>>>>> represented syntactically to be computable
>>>> Meaningless gobbledy-good until you actually define what you mean
>>>> and spell out the actual rules that need to be followed.
>>>>
>>>> Note, "Computability" is actually a fairly late in the process
>>>> concept. You first need to show that you logic can actually do
>>>> something useful
>>>>
>>>>>
>>>>>> To just try to change things at the end is just PROOF that your
>>>>>> "Correct Reasoning" has to not be based on any real principles of
>>>>>> logic.
>>>>>>
>>>>>> Since it is clear that you want to change some of the basics of
>>>>>> how logic works, you are not allowed to just use ANY of classical
>>>>>> logic until you actually show what part of it is still usable
>>>>>> under your system and what changes happen.
>>>>>>
>>>>>
>>>>> Whenever an expression of language is derived as the semantic
>>>>> consequence of other expressions of language we have valid inference.
>>>>
>>>> And, are you using the "classical" definition of "semantic" (which
>>>> makes this sentence somewhat cirular) or do you mean something based
>>>> on the concept you sometimes use of  "the meaning of the words".
>>>>
>>>
>>> *Principle of explosion*
>>> An alternate argument for the principle stems from model theory. A
>>> sentence P is a semantic consequence of a set of sentences Γ only if
>>> every model of Γ is a model of P. However, there is no model of the
>>> contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
>>> that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P) is a
>>> model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>
>>> Vacuous truth does not count as truth.
>>> All variables must be quantified
>>>
>>> "all cell phones in the room are turned off" will be true when no
>>> cell phones are in the room.
>>>
>>> ∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))
>>>
>>>
>>>>>
>>>>> The semantic consequence must be specified syntactically so that it
>>>>> can
>>>>> be computed or examined in formal systems.
>>>>>
>>>>> Just like in sound deductive inference when the premises are known
>>>>> to be
>>>>> true, and the reasoning valid (a semantic consequence) then the
>>>>> conclusion is necessarily true.
>>>>
>>>> So, what is the difference in your system from classical Formal Logic?
>>>>
>>>
>>> Semantic Necessity operator: ⊨□
>>>
>>>     FALSE ⊨□ FALSE // POE abolished
>>> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>>>
>>> ⇒ and → symbols are replaced by ⊨□
>>>
>>> The sets that the variables range over must be defined
>>> all variables must be quantified
>>>
>>> // x is a semantic consequence of its premises in L
>>> Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)
>>>
>>> // x is a semantic consequence of the axioms of L
>>> True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)
>>>
>>> *The above is all that I know right now*
>>>
>>>
>>>>> The most important aspect of the tiny little foundation of a formal
>>>>> system that I already specified immediately above is self-evident:
>>>>> True(L,X) can be defined and incompleteness is impossible.
>>>>
>>>> I don't think your system is anywhere near establish far enough for
>>>> you to say that.
>>>
>>> Try and show exceptions to this rule and I will fill in any gaps that
>>> you find.
>>>
>>> G asserts its own unprovability in F
>>> The reason that G cannot be proved in F is that this requires a
>>> sequence of inference steps in F that proves no such sequence
>>> of inference steps exists in F.
>>>
>>>
>> ∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
>> ∄sequence_of_inference_steps ⊆ F)
>>
>>
>
> So, you don't understand the differnce between the INFINITE set of
> sequence steps that show that G is True, and the FINITE number of steps
> that need to be shown to make G provable.
>

On 4/24/2023 6:35 PM, Richard Damon wrote:
> On 4/24/23 11:25 AM, olcott wrote:
>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>> On 4/22/23 6:49 PM, olcott wrote:
>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>
>>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>>> erroneous.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>>>> that claim is erroneous.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>
>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Any proof of G in F requires a sequence of inference steps in
>>>>>>>>>> F that
>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>
>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>> true but not provable in F.
>>>>>>>>>
>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>
>>>>>>>> To prove G in F you do.
>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> So, you don't understand how to prove that something is "True in
>>>>>>> F" by doing the steps in Meta-F.
>>>>>>>
>>>>>>
>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>> expressed in his theory is true in his meta-theory.
>>>>>
>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>> then the Liar's paradox would be true, thus that assumption can not
>>>>> be true.
>>>>>
>>>>
>>>> When one level of indirect reference is applied to the Liar Paradox it
>>>> becomes actually true. There was no "if".
>>>>
>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>
>>>>> Your
>>>>>
>>>>>>
>>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>>> G cannot be proved in F because this requires a sequence of inference
>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>
>>>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>>>> Meta-F, that G is true in F, and that G is unprovable in F, which
>>>>> is what is required.
>>>>>
>>>>
>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>> because this requires a sequence of inference steps in F that prove
>>>> that
>>>> they themselves do not exist.
>>>>
>>>> Meta-F merely removes the self-contradiction the same way Tarski's
>>>> Meta-
>>>> theory removed the self-contradiction.
>>>>
>>>>
>>>>> You are just showing that your mind can't handle the basics of
>>>>> logic, or truth.
>>>>>
>>>>
>>>> It may seem that way to someone that learns things by rote and mistakes
>>>> this for actual understanding of exactly how all of the elements of a
>>>> proof fit together coherently or fail to do so.
>>>>
>>>>> It sounds like you are too stupid to learn, and that you have
>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>
>>>>> If you won't even try to learn the basics, you have just condemned
>>>>> yourself into being a pathological liar because you just don't any
>>>>> better.
>>>>>
>>>>
>>>> I do at this point need to understand model theory very thoroughly.
>>>>
>>>> Learning the details of these things could have boxed me into a corner
>>>> prior to my philosophical investigation of seeing how the key elements
>>>> fail to fit together coherently.
>>>>
>>>> It is true that the set of analytical truth is simply a set of semantic
>>>> tautologies. It is true that formal systems grounded in this foundation
>>>> cannot be incomplete nor have any expressions of language that are
>>>> undecidable. Now that I have this foundation I have a way to see
>>>> exactly
>>>> how the concepts of math diverge from correct reasoning.
>>>>
>>>>>>
>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>> cannot be
>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>>>>>> proved in Tarski's theory.
>>>>>>
>>>>>
>>>>> Which he didn't do, but you are too stupid to understand claissic
>>>>> arguement forms.
>>>>>
>>>>
>>>> It is not that I do not understand, it is that I can directly see
>>>> where and how formal mathematical systems diverge from correct
>>>> reasoning.
>>>
>>> But since you are discussing Formal Logic, you need to use the rules
>>> of Formal logic.
>>>
>>> The other way to say it is that your "Correct Reasoning" diverges
>>> from the accepted and proven system of Formal Logic.
>>
>>
>>
>> In classical logic, intuitionistic logic and similar logical systems,
>> the principle of explosion
>>
>> ex falso [sequitur] quodlibet,
>> 'from falsehood, anything [follows]'
>>
>> ex contradictione [sequitur] quodlibet,
>> 'from contradiction, anything [follows]')
>
> Right, if a logic system can prove a contradiction, that out of that
> contradiction you can prove anything
>
>>
>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> ∴ FALSE ⊢ Donald Trump is the Christ
>> ∴ FALSE ⊢ Donald Trump is Satan
>
> Which isn't what was being talked about.
>
> You clearly don't understand how the principle of explosion works, which
> isn't surprising considering how many misconseptions you have about how
> logic works.
>

ex falso [sequitur] quodlibet,'from falsehood, anything [follows]'
∴ FALSE ⊢ Donald Trump is the Christ

> Right now, I would say you are to ignorant on that basics of logic to be
> able to explain, even in basic terms, how it works, you have shown
> yourself to be that stupid.
>
>
>>
>> *Correction abolishing the POE nonsense*
>> Semantic Necessity operator: ⊨□
>> FALSE ⊨□ FALSE
>> (P ∧ ¬P) ⊨□ FALSE
>>
>
> So, FULLY define what you mean by that.
>

The two logic symbols already say semantic necessity, model theory may
have screwed up the idea of semantics by allowing vacuous truth.
I must become a master expert of at least basic model theory.

>>
>>>>
>>>> Because you are a learned-by-rote person you make sure to never examine
>>>> whether or not any aspect of math diverges from correct reasoning, you
>>>> simply assume that math is the gospel even when it contradicts itself.
>>>
>>> Nope, I know that with logic, if you follow the rules, you will get
>>> the correct answer by the rules.
>>>
>>
>> Then you must agree that Trump is the Christ and Trump is Satan both of
>> those were derived from correct logic.
>>
>>> If you break the rules, you have no idea where you will go.
>>>
>>> As I have told you before, if you want to see what your "Correct
>>> Reasoning" can do as a replaceent logic system, you need to start at
>>> the BEGINNING, and see wht it gets.
>>>
>>
>> I would be happy to talk this through with you.
>>
>> The beginning is that
>>
>> valid inference an expression X of language L must be a semantic
>> consequence of its premises in L
>
>
> And what do you mean by "semantic"
>

On 4/24/2023 6:35 PM, Richard Damon wrote:
> On 4/24/23 10:40 AM, olcott wrote:
>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>> On 4/22/23 6:10 PM, olcott wrote:
>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>> erroneous.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>> that claim is erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>
>>>>>>> But Godel's G doesn't do that.
>>>>>>>
>>>>>>>>
>>>>>>>> Any proof of G in F requires a sequence of inference steps in F
>>>>>>>> that
>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>
>>>>>>> It is of course impossible to prove in F that a statement is true
>>>>>>> but not provable in F.
>>>>>>>
>>>>>>> You don't need to do the proof in F,
>>>>>>
>>>>>> To prove G in F you do.
>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>
>>>>>>
>>>>>
>>>>> So, you don't understand how to prove that something is "True in F"
>>>>> by doing the steps in Meta-F.
>>>>>
>>>>
>>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>>> in his theory is true in his meta-theory.
>>>
>>> No, he didn't, he showed that *IF* a certain assuption was true, then
>>> the Liar's paradox would be true, thus that assumption can not be true.
>>>
>>> Your
>>>
>>>>
>>>> We can do the same thing when G asserts its own unprovability in F.
>>>> G cannot be proved in F because this requires a sequence of inference
>>>> steps in F that prove that they themselves do not exist in F.
>>>
>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>>> what is required.
>>>
>>> You are just showing that your mind can't handle the basics of logic, or
>>
>> Proving that G is true in F requires a sequence of inference steps that
>> prove that they themselves don't exist.
>>
>> You might be bright enough to understand that is self-contradictory.
>>
>
> Except that G is proved in Meta-F to be "True in F".

When you assume that infinite proofs are not a thing then
When you understood rather than ignore that a proof of G in F requires a
sequence of inference steps in F that prove that they themselves don't
exist then and only then is it possible to understand that a proof of G
in F cannot be done only because it is self-contradictory.

Ignoring this doesn't make it go away. Assuming this it is not needed
requires another way of proving in F that G cannot be proved in F.
An infinite proof is always impossible so that way is out.

>
> With a finite number of steps in Meta-F, we can prove that the infinite
> number of steps in F exist and are true.
>

That is cheating. The purpose here is to see WHY rather than merely THAT
G is unprovable in F.

> In particular, in F, we need to check every number individual to see if
> it satisfies the relationship, and we have no short cut to make this
> operation finite,

Then it doesn't count for jack shit. You might as well resort to a magic
fairy waving a magic wand.

> so we can't prove it. But in Meta-F, we know something
> about the relationship, and are able to prove that no number can satisfy
> the relationship, and do so in a finite number of steps.
>

When we write G in Meta-F to begin with then Meta-F can recognize the
contradiction and report the non-sequitur error.

> Thus, we can prove in Meta-F that G must be true in F.
>
> The sequence of steps in F is infinite, so not a proof in F.
>
> In fact, in Meta-F we are also able to prove that there CAN'T be a
> finite sequence set of steps that prove G true in F.
>
> Thus, with logic in Meta-F, we can prove that, G is True in F and can
> not be proven in F.
>
> You just don't seem to understand how Meta-Logic works. And, it turns
> out, that meta-logic is a very important tool for proving things, so
> this is one of your Kryponites.
>

Actually I understand how Meta-F works better than most. We need no F
and Meta-F we write G in Meta-F to begin with and it rejects G as
semantically erroneous.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/25/23 12:17 AM, olcott wrote:
> On 4/24/2023 6:35 PM, Richard Damon wrote:
>> On 4/24/23 10:40 AM, olcott wrote:
>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>> erroneous.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Since you don't understand the meaning of self-contradictory,
>>>>>>>>>> that claim is erroneous.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>
>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Any proof of G in F requires a sequence of inference steps in F
>>>>>>>>> that
>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>
>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>> true but not provable in F.
>>>>>>>>
>>>>>>>> You don't need to do the proof in F,
>>>>>>>
>>>>>>> To prove G in F you do.
>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> So, you don't understand how to prove that something is "True in
>>>>>> F" by doing the steps in Meta-F.
>>>>>>
>>>>>
>>>>> I just showed you how Tarski proved that the Liar Paradox expressed
>>>>> in his theory is true in his meta-theory.
>>>>
>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>> then the Liar's paradox would be true, thus that assumption can not
>>>> be true.
>>>>
>>>> Your
>>>>
>>>>>
>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>> G cannot be proved in F because this requires a sequence of inference
>>>>> steps in F that prove that they themselves do not exist in F.
>>>>
>>>> Right, you can't prove, in F, that G is true, but you can prove, in
>>>> Meta-F, that G is true in F, and that G is unprovable in F, which is
>>>> what is required.
>>>>
>>>> You are just showing that your mind can't handle the basics of
>>>> logic, or
>>>
>>> Proving that G is true in F requires a sequence of inference steps that
>>> prove that they themselves don't exist.
>>>
>>> You might be bright enough to understand that is self-contradictory.
>>>
>>
>> Except that G is proved in Meta-F to be "True in F".
>
> When you assume that infinite proofs are not a thing then

The aren't, by DEFINITION. It is a basic piece of Knowledge theory. You
can only know something showable in finite steps since we are only finite.

> When you understood rather than ignore that a proof of G in F requires a
> sequence of inference steps in F that prove that they themselves don't
> exist then and only then is it possible to understand that a proof of G
> in F cannot be done only because it is self-contradictory.
>
> Ignoring this doesn't make it go away. Assuming this it is not needed
> requires another way of proving in F that G cannot be proved in F.
> An infinite proof is always impossible so that way is out.

And you seem to not understand how knowledge works.

G can not be proven in F, because F doesn't have the tools to allow us
to construct the needed finite proof.

G can be TRUE in F, as Truth doesn't require that it be knowable in the
field, just that its truth is established by a, possible infinite, set
of connections to the truth makers.

G can be KNOWN True in F, because it can be proven in Meta-F, which has
additional knowledge about F, that allows us to perform in finite steps
in Meta-F things that take an infinte number of steps in F. Because
Meta-F knows about F, it can show what knowledge in Meta-F can be
transfered to include in F.

By the same token, we can show in Meta-F that G can not be proven in F,
and that this Knowledge can be transfered to include in F

>
>>
>> With a finite number of steps in Meta-F, we can prove that the
>> infinite number of steps in F exist and are true.
>>
>
> That is cheating. The purpose here is to see WHY rather than merely THAT
> G is unprovable in F.
>

G is unprovable, because if you could prove it, then it couldn't be true.

WHY is a much harder questing that IS.

>> In particular, in F, we need to check every number individual to see
>> if it satisfies the relationship, and we have no short cut to make
>> this operation finite,
>
> Then it doesn't count for jack shit. You might as well resort to a magic
> fairy waving a magic wand.

Why? We have shown in Meta-F that an infinite sequence of steps exist in
F to show that G is true.

You just are too stupid to understand it.

>
>> so we can't prove it. But in Meta-F, we know something about the
>> relationship, and are able to prove that no number can satisfy the
>> relationship, and do so in a finite number of steps.
>>
>
> When we write G in Meta-F to begin with then Meta-F can recognize the
> contradiction and report the non-sequitur error.

Nope, we find that G is True in F and Meta-F, not provable in F, but
provable in Meta-F.

>
>> Thus, we can prove in Meta-F that G must be true in F.
>>
>> The sequence of steps in F is infinite, so not a proof in F.
>>
>> In fact, in Meta-F we are also able to prove that there CAN'T be a
>> finite sequence set of steps that prove G true in F.
>>
>> Thus, with logic in Meta-F, we can prove that, G is True in F and can
>> not be proven in F.
>>
>> You just don't seem to understand how Meta-Logic works. And, it turns
>> out, that meta-logic is a very important tool for proving things, so
>> this is one of your Kryponites.
>>
>
> Actually I understand how Meta-F works better than most. We need no F
> and Meta-F we write G in Meta-F to begin with and it rejects G as
> semantically erroneous.
>

Which shows you don't understand Meta-F.

PERIOD.

A wise man knows what he doesn't know.

A fool thinks he knows what he doesn't know.

On 4/25/23 12:03 AM, olcott wrote:
> On 4/24/2023 6:35 PM, Richard Damon wrote:
>> On 4/24/23 11:25 AM, olcott wrote:
>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making it
>>>>>>>>>>>>> erroneous.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>
>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps in
>>>>>>>>>>> F that
>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>
>>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>>> true but not provable in F.
>>>>>>>>>>
>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>
>>>>>>>>> To prove G in F you do.
>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> So, you don't understand how to prove that something is "True in
>>>>>>>> F" by doing the steps in Meta-F.
>>>>>>>>
>>>>>>>
>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>
>>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>>> then the Liar's paradox would be true, thus that assumption can
>>>>>> not be true.
>>>>>>
>>>>>
>>>>> When one level of indirect reference is applied to the Liar Paradox it
>>>>> becomes actually true. There was no "if".
>>>>>
>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>
>>>>>> Your
>>>>>>
>>>>>>>
>>>>>>> We can do the same thing when G asserts its own unprovability in F.
>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>> inference
>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>
>>>>>> Right, you can't prove, in F, that G is true, but you can prove,
>>>>>> in Meta-F, that G is true in F, and that G is unprovable in F,
>>>>>> which is what is required.
>>>>>>
>>>>>
>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>> because this requires a sequence of inference steps in F that prove
>>>>> that
>>>>> they themselves do not exist.
>>>>>
>>>>> Meta-F merely removes the self-contradiction the same way Tarski's
>>>>> Meta-
>>>>> theory removed the self-contradiction.
>>>>>
>>>>>
>>>>>> You are just showing that your mind can't handle the basics of
>>>>>> logic, or truth.
>>>>>>
>>>>>
>>>>> It may seem that way to someone that learns things by rote and
>>>>> mistakes
>>>>> this for actual understanding of exactly how all of the elements of a
>>>>> proof fit together coherently or fail to do so.
>>>>>
>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>
>>>>>> If you won't even try to learn the basics, you have just condemned
>>>>>> yourself into being a pathological liar because you just don't any
>>>>>> better.
>>>>>>
>>>>>
>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>
>>>>> Learning the details of these things could have boxed me into a corner
>>>>> prior to my philosophical investigation of seeing how the key elements
>>>>> fail to fit together coherently.
>>>>>
>>>>> It is true that the set of analytical truth is simply a set of
>>>>> semantic
>>>>> tautologies. It is true that formal systems grounded in this
>>>>> foundation
>>>>> cannot be incomplete nor have any expressions of language that are
>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>> exactly
>>>>> how the concepts of math diverge from correct reasoning.
>>>>>
>>>>>>>
>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>> cannot be
>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot
>>>>>>> be proved in Tarski's theory.
>>>>>>>
>>>>>>
>>>>>> Which he didn't do, but you are too stupid to understand claissic
>>>>>> arguement forms.
>>>>>>
>>>>>
>>>>> It is not that I do not understand, it is that I can directly see
>>>>> where and how formal mathematical systems diverge from correct
>>>>> reasoning.
>>>>
>>>> But since you are discussing Formal Logic, you need to use the rules
>>>> of Formal logic.
>>>>
>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>> from the accepted and proven system of Formal Logic.
>>>
>>>
>>>
>>> In classical logic, intuitionistic logic and similar logical systems,
>>> the principle of explosion
>>>
>>> ex falso [sequitur] quodlibet,
>>> 'from falsehood, anything [follows]'
>>>
>>> ex contradictione [sequitur] quodlibet,
>>> 'from contradiction, anything [follows]')
>>
>> Right, if a logic system can prove a contradiction, that out of that
>> contradiction you can prove anything
>>
>>>
>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>
>>> ∴ FALSE ⊢ Donald Trump is the Christ
>>> ∴ FALSE ⊢ Donald Trump is Satan
>>
>> Which isn't what was being talked about.
>>
>> You clearly don't understand how the principle of explosion works,
>> which isn't surprising considering how many misconseptions you have
>> about how logic works.
>>
>
> ex falso [sequitur] quodlibet,'from falsehood, anything [follows]'
> ∴ FALSE ⊢ Donald Trump is the Christ

On 4/24/23 11:28 PM, olcott wrote:
> On 4/24/2023 6:35 PM, Richard Damon wrote:
>> On 4/24/23 12:13 PM, olcott wrote:
>>> On 4/24/2023 10:58 AM, olcott wrote:
>>>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>>>>> On 4/22/23 7:57 PM, olcott wrote:
>>>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making
>>>>>>>>>>>>>>>> it erroneous.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>>>
>>>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps
>>>>>>>>>>>>>> in F that
>>>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>>>
>>>>>>>>>>>>> It is of course impossible to prove in F that a statement
>>>>>>>>>>>>> is true but not provable in F.
>>>>>>>>>>>>>
>>>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>>>
>>>>>>>>>>>> To prove G in F you do.
>>>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So, you don't understand how to prove that something is "True
>>>>>>>>>>> in F" by doing the steps in Meta-F.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>>>
>>>>>>>>> No, he didn't, he showed that *IF* a certain assuption was
>>>>>>>>> true, then the Liar's paradox would be true, thus that
>>>>>>>>> assumption can not be true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When one level of indirect reference is applied to the Liar
>>>>>>>> Paradox it
>>>>>>>> becomes actually true. There was no "if".
>>>>>>>>
>>>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>>>
>>>>>>>>> Your
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> We can do the same thing when G asserts its own unprovability
>>>>>>>>>> in F.
>>>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>>>> inference
>>>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>>>
>>>>>>>>> Right, you can't prove, in F, that G is true, but you can
>>>>>>>>> prove, in Meta-F, that G is true in F, and that G is unprovable
>>>>>>>>> in F, which is what is required.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>>>>> because this requires a sequence of inference steps in F that
>>>>>>>> prove that
>>>>>>>> they themselves do not exist.
>>>>>>>>
>>>>>>>> Meta-F merely removes the self-contradiction the same way
>>>>>>>> Tarski's Meta-
>>>>>>>> theory removed the self-contradiction.
>>>>>>>>
>>>>>>>>
>>>>>>>>> You are just showing that your mind can't handle the basics of
>>>>>>>>> logic, or truth.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It may seem that way to someone that learns things by rote and
>>>>>>>> mistakes
>>>>>>>> this for actual understanding of exactly how all of the elements
>>>>>>>> of a
>>>>>>>> proof fit together coherently or fail to do so.
>>>>>>>>
>>>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>>>
>>>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>>>> just don't any better.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>>>>
>>>>>>>> Learning the details of these things could have boxed me into a
>>>>>>>> corner
>>>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>>>> elements
>>>>>>>> fail to fit together coherently.
>>>>>>>>
>>>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>>>> semantic
>>>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>>>> foundation
>>>>>>>> cannot be incomplete nor have any expressions of language that are
>>>>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>>>>> exactly
>>>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>>>>> cannot be
>>>>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox
>>>>>>>>>> cannot be proved in Tarski's theory.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Which he didn't do, but you are too stupid to understand
>>>>>>>>> claissic arguement forms.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is not that I do not understand, it is that I can directly
>>>>>>>> see where and how formal mathematical systems diverge from
>>>>>>>> correct reasoning.
>>>>>>>
>>>>>>> But since you are discussing Formal Logic, you need to use the
>>>>>>> rules of Formal logic.
>>>>>>>
>>>>>>
>>>>>> I have never been talking about formal logic. I have always been
>>>>>> talking
>>>>>> about the philosophical foundations of correct reasoning.
>>>>>
>>>>> No, you have been talking about theorys DEEP in formal logic. You
>>>>> can't talk about the "errors" in those theories, with being in
>>>>> formal logic.
>>>>>
>>>>> IF you think you can somehow talk about the foundations, while
>>>>> working in the penthouse, you have just confirmed that you do not
>>>>> understand how ANY form of logic works.
>>>>>
>>>>> PERIOD.
>>>>>
>>>>>
>>>>>>
>>>>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>>>>> from the accepted and proven system of Formal Logic.
>>>>>>>
>>>>>>
>>>>>> It is correct reasoning in the absolute sense that I refer to.
>>>>>> If anyone has the opinion that arithmetic does not exist they are
>>>>>> incorrect in the absolute sense of the word: "incorrect".
>>>>>>
>>>>>
>>>>> IF you reject the logic that a theory is based on, you need to
>>>>> reject the logic system, NOT the theory.
>>>>>
>>>>> You are just showing that you have wasted your LIFE because you
>>>>> don'tunderstnad how to work ligic.
>>>>>
>>>>>>>>
>>>>>>>> Because you are a learned-by-rote person you make sure to never
>>>>>>>> examine
>>>>>>>> whether or not any aspect of math diverges from correct
>>>>>>>> reasoning, you
>>>>>>>> simply assume that math is the gospel even when it contradicts
>>>>>>>> itself.
>>>>>>>
>>>>>>> Nope, I know that with logic, if you follow the rules, you will
>>>>>>> get the correct answer by the rules.
>>>>>>>
>>>>>>> If you break the rules, you have no idea where you will go.
>>>>>>>
>>>>>>
>>>>>> In other words you never ever spend any time on making sure that
>>>>>> these
>>>>>> rules fit together coherently.
>>>>>
>>>>> The rules work together just fine.
>>>>>
>>>>> YOU don't like some of the results, but they work just fine for
>>>>> most of the field.
>>>>>
>>>>> You are just PROVING that you have no idea how to actually discuss
>>>>> a new foundation for logic, likely because you are incapable of
>>>>> actually comeing up with a consistent basis for working logic.
>>>>>
>>>>>>
>>>>>>> As I have told you before, if you want to see what your "Correct
>>>>>>> > Reasoning" can do as a replaceent logic system, you need to
>>>>>>> start at the
>>>>>>> BEGINNING, and see wht it gets.
>>>>>>>
>>>>>>
>>>>>> The foundation of correct reasoning is that the entire body of
>>>>>> analytical truth is a set of semantic tautologies.
>>>>>>
>>>>>> This means that all correct inference always requires determining the
>>>>>> semantic consequence of expressions of language. This semantic
>>>>>> consequence can be specified syntactically, and indeed must be
>>>>>> represented syntactically to be computable
>>>>> Meaningless gobbledy-good until you actually define what you mean
>>>>> and spell out the actual rules that need to be followed.
>>>>>
>>>>> Note, "Computability" is actually a fairly late in the process
>>>>> concept. You first need to show that you logic can actually do
>>>>> something useful
>>>>>
>>>>>>
>>>>>>> To just try to change things at the end is just PROOF that your
>>>>>>> "Correct Reasoning" has to not be based on any real principles of
>>>>>>> logic.
>>>>>>>
>>>>>>> Since it is clear that you want to change some of the basics of
>>>>>>> how logic works, you are not allowed to just use ANY of classical
>>>>>>> logic until you actually show what part of it is still usable
>>>>>>> under your system and what changes happen.
>>>>>>>
>>>>>>
>>>>>> Whenever an expression of language is derived as the semantic
>>>>>> consequence of other expressions of language we have valid inference.
>>>>>
>>>>> And, are you using the "classical" definition of "semantic" (which
>>>>> makes this sentence somewhat cirular) or do you mean something
>>>>> based on the concept you sometimes use of  "the meaning of the words".
>>>>>
>>>>
>>>> *Principle of explosion*
>>>> An alternate argument for the principle stems from model theory. A
>>>> sentence P is a semantic consequence of a set of sentences Γ only if
>>>> every model of Γ is a model of P. However, there is no model of the
>>>> contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
>>>> that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P) is a
>>>> model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>
>>>> Vacuous truth does not count as truth.
>>>> All variables must be quantified
>>>>
>>>> "all cell phones in the room are turned off" will be true when no
>>>> cell phones are in the room.
>>>>
>>>> ∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))
>>>>
>>>>
>>>>>>
>>>>>> The semantic consequence must be specified syntactically so that
>>>>>> it can
>>>>>> be computed or examined in formal systems.
>>>>>>
>>>>>> Just like in sound deductive inference when the premises are known
>>>>>> to be
>>>>>> true, and the reasoning valid (a semantic consequence) then the
>>>>>> conclusion is necessarily true.
>>>>>
>>>>> So, what is the difference in your system from classical Formal Logic?
>>>>>
>>>>
>>>> Semantic Necessity operator: ⊨□
>>>>
>>>>     FALSE ⊨□ FALSE // POE abolished
>>>> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>>>>
>>>> ⇒ and → symbols are replaced by ⊨□
>>>>
>>>> The sets that the variables range over must be defined
>>>> all variables must be quantified
>>>>
>>>> // x is a semantic consequence of its premises in L
>>>> Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)
>>>>
>>>> // x is a semantic consequence of the axioms of L
>>>> True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)
>>>>
>>>> *The above is all that I know right now*
>>>>
>>>>
>>>>>> The most important aspect of the tiny little foundation of a formal
>>>>>> system that I already specified immediately above is self-evident:
>>>>>> True(L,X) can be defined and incompleteness is impossible.
>>>>>
>>>>> I don't think your system is anywhere near establish far enough for
>>>>> you to say that.
>>>>
>>>> Try and show exceptions to this rule and I will fill in any gaps that
>>>> you find.
>>>>
>>>> G asserts its own unprovability in F
>>>> The reason that G cannot be proved in F is that this requires a
>>>> sequence of inference steps in F that proves no such sequence
>>>> of inference steps exists in F.
>>>>
>>>>
>>> ∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
>>> ∄sequence_of_inference_steps ⊆ F)
>>>
>>>
>>
>> So, you don't understand the differnce between the INFINITE set of
>> sequence steps that show that G is True, and the FINITE number of
>> steps that need to be shown to make G provable.
>>
>
> The experts seem to believe that unless a proof can be transformed into
> a finite sequence of steps it is no actual proof at all. Try and cite a
> source that says otherwise.