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.

>
> 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.

>
> You are so sure that I must be wrong that you don't bother to understand
> what I am saying.

No, I understand what you are saying and see where you are WRONG.

>
> It seem that the time has come for me to spend the little time that it
> takes to understand the technical details of Gödel's proof.
>
> I am estimating that have very good understanding of the preface to the
> proof and the SEP article should provide this.
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>
>