On 4/27/2023 6:19 AM, Richard Damon wrote:
> On 4/26/23 10:47 PM, olcott wrote:
>> On 4/26/2023 7:07 AM, Richard Damon wrote:
>>> 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.
>>>
>>> No, to change the rules you have to go back to the beginning.
>>>
>>
>> Non_Sequitur(G) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>
>
> No, Non_Sequitur: Most of what Peter Olcott says.
>
> You still can't change the rules without going back to the beginning,

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.
>

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.
>

On 4/27/23 9:07 PM, olcott wrote:

> The standard definition of mathematical incompleteness:
> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))

Remember, that if φ ∈ F then φ has a defined truth value in F, it is
either True of False, and thus can't be the "Liar's Paradox".

>
> Requires formal systems to do the logically impossible:
> to prove self-contradictory expressions of language.

Nope. You don't understand what the words mean.

Remember, incompleteness only happens if a TRUE statement can't be
proven, an actual "self-contradictory" statment won't be true.

(or is FALSE and can't be proven to be false, which is basically the
same thing).

>
> So formal systems are "incomplete" in the same sense that we determine
> that a baker that cannot bake a proper angel food cake using ordinary
> red house bricks as the only ingredient lacks sufficient baking skill.
>

Nope, becuase they are only inclomplete if a statement that is TRUE
can't be proven.

You just don't understand that,

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.

On 4/27/2023 9:41 PM, Richard Damon wrote:
> On 4/27/23 9:07 PM, olcott wrote:
>
>> The standard definition of mathematical incompleteness:
>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Remember, that if φ ∈ F then φ has a defined truth value in F, it is
> either True of False, and thus can't be the "Liar's Paradox".
>
>

How about this one?
Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))

>>
>> Requires formal systems to do the logically impossible:
>> to prove self-contradictory expressions of language.
>
> Nope. You don't understand what the words mean.

That part I have correctly and Gödel acknowledged the self-contradictory
expressions ... can likewise be used for a similar undecidability proof...

....14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
(Gödel 1931:40)

Antinomy
....term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy

> Remember, incompleteness only happens if a TRUE statement can't be
> proven, an actual "self-contradictory" statment won't be true.
>

You have that incorrectly too.
When G asserts its own unprovability in F the proof of G in F requires a
sequence of inference steps in F that prove that they themselves do not
exist.

Gödel’s Theorem, as a simple corollary of Proposition VI (p. 57) is
frequently called, proves that there are arithmetical propositions which
are undecidable (i.e. neither provable nor disprovable) within their
arithmetical system, and the proof proceeds by actually specifying such
a proposition, namely the proposition g expressed by the formula to
which “17 Gen r” refers (p. 58). g is an arithmetical proposition; but
the proposition that g is undecidable within the system is not an
arithmetical proposition, since it is concerned with provability within
an arithmetical system, and this is a meta-arithmetical and not an
arithmetical notion. Gödel’s Theorem is thus a result which belongs not
to mathematics but to metamathematics, the name given by Hilbert to the
study of rigorous proof in mathematics and symbolic logic

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

> (or is FALSE and can't be proven to be false, which is basically the
> same thing).
>
>>
>> So formal systems are "incomplete" in the same sense that we determine
>> that a baker that cannot bake a proper angel food cake using ordinary
>> red house bricks as the only ingredient lacks sufficient baking skill.
>>
>
> Nope, becuase they are only inclomplete if a statement that is TRUE
> can't be proven.
>

The liar paradox is self contradictory when applied to itself is not
self-contradictory when applied to another different instance of itself.

This sentence is not true: "This sentence is not true"
inner one is neither true nor false
outer one is true because the inner one is neither true nor false

When G asserts its own unprovability in F the proof of G in F requires a
sequence of inference steps in F that prove that they themselves do not
exist. metamathematics, can see that G cannot be proved in F.

> You just don't understand that,
>

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

On 4/28/23 12:23 AM, olcott wrote:
> On 4/27/2023 9:41 PM, Richard Damon wrote:
>> On 4/27/23 9:07 PM, olcott wrote:
>>
>>> The standard definition of mathematical incompleteness:
>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>
>> Remember, that if φ ∈ F then φ has a defined truth value in F, it is
>> either True of False, and thus can't be the "Liar's Paradox".
>>
>>
>
> How about this one?
> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))

You use of terms that you do not define doesn't help you.

Incomplete means, in actual words, that there exists a true statement in
F that can not be proven in F, or similarly a False statement in F that
can not be disproven (proven to be false).

Incompleteness is NOT about statements that meet the "syntax" of F, but
might not actually be Truthbearers. Of course you can't prove or refute
a non-truthbearer (at best you might be able to show it is a
non-truthbearer).

Trying to use ANY other definition that isn't actually equivalent is
just proof that you don't understand the rules of logic and have fallen
to a strawman.

>
>>>
>>> Requires formal systems to do the logically impossible:
>>> to prove self-contradictory expressions of language.
>>
>> Nope. You don't understand what the words mean.
>
> That part I have correctly and Gödel acknowledged the self-contradictory
> expressions ... can likewise be used for a similar undecidability proof...

And none of those are directly about G in F.

>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...
> (Gödel 1931:40)

Yep, you can use the FORM of any epistemolgoical antinomy, converting it
from a statement about its own truth to being about its own provability,
to get a similar proof.

>
> Antinomy
> ...term often used in logic and epistemology, when describing a paradox
> or unresolvable contradiction.
> https://www.newworldencyclopedia.org/entry/Antinomy
>
>> Remember, incompleteness only happens if a TRUE statement can't be
>> proven, an actual "self-contradictory" statment won't be true.
>>
>
> You have that incorrectly too.
> When G asserts its own unprovability in F the proof of G in F requires a
> sequence of inference steps in F that prove that they themselves do not
> exist.

But G DOESN'T "asserts its own unprovability in F", and G is not proven
"in F".

You statement just shows that you don't understand the proof and are
totally missing that almost all of the paper is written from the aspect
of Meta-F.

>
> Gödel’s Theorem, as a simple corollary of Proposition VI (p. 57) is
> frequently called, proves that there are arithmetical propositions which
> are undecidable (i.e. neither provable nor disprovable) within their
> arithmetical system, and the proof proceeds by actually specifying such
> a proposition, namely the proposition g expressed by the formula to
> which “17 Gen r” refers (p. 58). g is an arithmetical proposition; but
> the proposition that g is undecidable within the system is not an
> arithmetical proposition, since it is concerned with provability within
> an arithmetical system, and this is a meta-arithmetical and not an
> arithmetical notion. Gödel’s Theorem is thus a result which belongs not
> to mathematics but to metamathematics, the name given by Hilbert to the
> study of rigorous proof in mathematics and symbolic logic
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Yes, Hilbert had simillar errors in logic, which he, I believe,
eventaully realized. Yes, much of Godel's proof could be described as
"meta-mathematics", but that meta- shows that IN MATHEMATICS ITSELF,
there exist propositions that are true but can not be proven within
mathematics. Thus, mathematics meets the requirements to be called
"incomplete"

>
>> (or is FALSE and can't be proven to be false, which is basically the
>> same thing).
>>
>>>
>>> So formal systems are "incomplete" in the same sense that we determine
>>> that a baker that cannot bake a proper angel food cake using ordinary
>>> red house bricks as the only ingredient lacks sufficient baking skill.
>>>
>>
>> Nope, becuase they are only inclomplete if a statement that is TRUE
>> can't be proven.
>>
>
> The liar paradox is self contradictory when applied to itself is not
> self-contradictory when applied to another different instance of itself.

So, you don't understand what the "Liar Paradox" actually is. It is, and
only is, a statement that asserts ITS OWN falsehood. It can't refer to a
"different instance" as either that other isn't "itself", so refering to
it makes this statement not the liar's paradox, or it actually IS
itself, and thus must have the same truth value. You don't seem to
understand the fundamental rule that if a copy of the statement is
considered to be "the same statement", that all those copies must. by
definition. have the same truth value.

>
> This sentence is not true: "This sentence is not true"
> inner one is neither true nor false
> outer one is true because the inner one is neither true nor false

But isn't the liar's paradox.

Again, you show you don't understand the actual meaning of the words.

>
> When G asserts its own unprovability in F the proof of G in F requires a
> sequence of inference steps in F that prove that they themselves do not
> exist. metamathematics, can see that G cannot be proved in F.

Exept that Godel's G doesn't "assert is own unprovability in F" nor is
"G proved in F" (in fact, Godel shows such a proof is impossible).

metamathematics can PROVE that Godel's statement G is TRUE IN
MATHEMATICS, but not provable there.

You don't seem to understand how meta-systems work and how they can
actaully prove things about the system they are a meta- for.

If you "Correct Reasoning" can't handle meta-logic, then you aren't
going to be able to prove much in it, as most major proofs actually use
meta-logic.

>
>
>> You just don't understand that,
>>
>

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
>
>
>

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
>