On 4/28/23 12:00 AM, olcott wrote:
> 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
>
>
>

So, you still don't understand the statement because you are just using
(never actually) learned by rote transformations.

Just shows your ignorance.