On 4/27/2023 9:41 PM, Richard Damon wrote:
> On 4/27/23 9:09 PM, olcott wrote:
>> On 4/27/2023 6:19 AM, Richard Damon wrote:
>>> On 4/26/23 10:41 PM, olcott wrote:
>>>> On 4/26/2023 7:07 AM, Richard Damon wrote:
>>>>> 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
>>>>>
>>>>> That isn't what the statment actually means, so you are just stupid.
>>>>>
>>>>>
>>>>>>
>>>>>> It is jack ass nonsense like this that proves the
>>>>>> principle of explosion is nothing even kludge
>>>>>
>>>>> Right, false doesn't PROVE anything, but implies anything,
>>>>
>>>>     "P, ¬P ⊢ Q For any statements P and Q, if P and not-P are both
>>>> true,
>>>>      then it logically follows that Q is true."
>>>>
>>>> https://en.wikipedia.org/wiki/Principle_of_explosion#Symbolic_representation
>>>>
>>>
>>> So, you don't understnad what you are reading.
>>>
>>> FALSE itself isn't proving anything.
>>>
>>
>> 'from falsehood, anything [follows]'
>> Is not saying that a FALSE antecedent implies any consequent.
>>
>
> That is EXACTLY what it is saying. That a false premise can be said to
> imply any consequent, since that implication only holds if the premise
> is actually true.
>
> You are just not understanding what the words actually mean, because you
> are ignorant by choice.

https://proofwiki.org/wiki/Rule_of_Explosion
Sequent Form ⊥ ⊢ ϕ

https://en.wikipedia.org/wiki/List_of_logic_symbols
⊥ falsum, ⊢ proves ϕ this logic sentence

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