On 12/11/2022 9:19 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 17:10:05 UTC+2, olcott wrote:
>>> No idea what you mean by 1 to ℕ
>> I did not use the math ℕ, I used N same as n.
> Yes. Those are called free/unbound variables!
>
> You are talking about the range [1..n]
> What is n?
>

A dead bullfrog?

> If n is unbound then [1..n] is not Valid(φ) !!!
>

n is any arbitrary integer > 0, thus excludes infinitary logic.
https://plato.stanford.edu/entries/logic-infinitary/

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/11/2022 9:21 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>> So which one is it?
>>>
>>> The disjunction requires a valid proof.
>>>
>> Unless φ is provable or refutable φ is not a logic expression.
> ERGO!!!
>
> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
>
>

Using my MTT one can construct an 1,2,3,4...n ary logic expression using
a slightly adapted FOL syntax.

https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF

By the theory of simple types I mean the doctrine which says that the
objects of thought (or, in another interpretation, the symbolic
expressions) are divided into types, namely: individuals, properties of
individuals, relations between individuals, properties of such
relations, etc. (with a similar hierarchy for extensions), and that
sentences of the form: " a has the property φ ", " b bears the relation
R to c ", etc. are meaningless, if a, b, c, R, φ are not of types
fitting together.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/11/22 7:23 AM, olcott wrote:
> On 12/11/2022 9:15 AM, Richard Damon wrote:
>> On 12/11/22 7:11 AM, olcott wrote:
>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>> So which one is it?
>>>>
>>>> The disjunction requires a valid proof.
>>>>
>>>
>>> Unless φ is provable or refutable φ is not a logic expression.
>>>
>>
>> Says Who? Provide a valid reference from someone knowlegable of the
>> field.
>>
>> You are using the wrong definitions of the terms.
>
>
> When everyone else uses to terms incorrectly then I seem like the black
> sheep of a herd of sheep. The sheep never notice their own group-think
> error. https://www.psychologytoday.com/us/basics/groupthink
>
> Truth itself is not a Democracy. Prior to Pythagoras there was a
> universal consensus that the Earth was flat. This does not make the
> Earth flat it merely means that everyone was wrong.
>

Right, EMPIRICAL truth is established outside of agreement, but based on
what is.

But, Theorems do not operate on the physical universe, but the agreed
upon universe of agreed logic. There is a difference by Logic Theories,
and Scientific Hypothosis/Theory.

IF everyone else uses a term one way, in a system based on agreement,
and one person uses it diffrerently, that one is BY DEFINITION, incorrect.

You seem to still have a fundamental lack of understanding of that which
you are talking about.

On 12/11/2022 9:24 AM, Richard Damon wrote:
> On 12/11/22 7:17 AM, olcott wrote:
>> On 12/11/2022 9:08 AM, Richard Damon wrote:
>>> On 12/11/22 5:53 AM, olcott wrote:
>>>> On 12/10/2022 10:19 PM, Richard Damon wrote:
>>>>> On 12/10/22 6:33 PM, olcott wrote:
>>>>>> On 12/10/2022 8:18 PM, Richard Damon wrote:
>>>>>>> On 12/10/22 5:59 PM, olcott wrote:
>>>>>>>> Theorem 1.
>>>>>>>> Every valid logical expression is provable. Equivalently, every
>>>>>>>> logical expression is either satisfiable or refutable.
>>>>>>>> https://plato.stanford.edu/entries/goedel/#ComThe
>>>>>>>>
>>>>>>>> The conventional definition of incompleteness:
>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>
>>>>>>>> Should actually be written as:
>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>> thus abolishing Incompleteness.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Did you notice what domain that Theorem was stated for?
>>>>>>>
>>>>>>> "First Order" deals with just a small limited subset of Mathematics.
>>>>>>>
>>>>>>> Yes, it is know that First Orders system can be complete, but can
>>>>>>> not express all the known properties of the Natural Numbers.
>>>>>>>
>>>>>>> Comutation Theory is NOT a "First Order Predicate Calculus" (it
>>>>>>> uses Higher Order logical predicated), so that Theorem doesn't
>>>>>>> apply.
>>>>>>
>>>>>> None-the-less its still applies to the philosophical foundation of
>>>>>> every
>>>>>> formal system. If an expression of formal or natural language is
>>>>>> neither
>>>>>> provable nor refutable then it is not a logical expression of any
>>>>>> kind
>>>>>> at all.
>>>>>>
>>>>>
>>>>> Nope. Shows you don't understand what you are talking about,
>>>>>
>>>>> Note, it isn't that True is DEFINED as provable, but that for many
>>>>> first order systems, it can be proven that all true statements can
>>>>> be proven.
>>>>>
>>>>> Yes, it is possible to include in a system an Axiom/Definition that
>>>>> says that all True Statements are Provable, and such a system needs
>>>>> to limit its logical capability, like it can only use first order
>>>>> predicates, or it will become inconsistent, and such inconsistancy
>>>>> might not be detectable within the system.
>>>>>
>>>>> Such a system can NOT handle the fullness of Mathematics, or
>>>>> systems like Computation Theory
>>>>>
>>>>
>>>> It handles the subset of computations that are decision problems
>>>> through the Curry Howard Isomorphism.
>>>
>>> No, Computation Theory uses logic operations not allowed
>>> withinvsystems that meet the requirements of the Completeness Theorem.
>>>
>>> Curry Howard also only applies in systems that HAVE programs, which
>>> aren't the sort of systems that the Completeness Theorem holds for.
>>>
>>> You are just showing you don't understand the concept of
>>> pre-requirements of a Theory.
>>>
>>
>> Every expression of language that cannot possibly resolve to true or
>> false is not a logic expression. The computation deriving the square
>> foot area of a house is not a logic expression.
>>
>>>>
>>>>>> Everyone that has been debating me on this forum does so entirely
>>>>>> on the
>>>>>> basis of learn-by-rote dogma.
>>>>>
>>>>> Nope, you have been arguing from never-learned-due-to-stupdity dogma.
>>>>>
>>>>> Your IGNORANCE does make your statements true.
>>>>>
>>>>>>
>>>>>> No one has considered that this math dogma might be inconsistent thus
>>>>>> incoherent when examined through its foundation basis.
>>>>>>
>>>>>
>>>>> No, you are just showing that you don't understanf what you are
>>>>> talking about.
>>>>
>>>> The conventional definition of incompleteness:
>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>
>>>> is wrong the correct way to say this is
>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>
>>>
>>> No, your "Valid" is just a restatement of Complete.
>>>
>>
>> You are ignoring GIGO: garbage in, garbage out.
>> Every self-contradictory expression of language that previously showed
>> that a formal system is incomplete actually shows that the expression
>> itself is garbage.
>
> No, YOU are talking GIGO since the expresions that you are refering to
> are NOT "Self-contradictory".
>
> The statement that "Statement X is not provable" is NOT a
> self-contradictory statement.

We are therefore confronted with a proposition which asserts
its own unprovability. (page 40/43)

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

X := "Statement X is not provable"

>
>>
>>> I don't know of a use of the Valid as applying to SYSTEMS, just
>>> arguments/proofs. The closes to Validity is Consistent, which means
>>> that no statement can be proven both True and False.
>>>
>>> There is nothing "Wrong" with an incomplete system that makes is not
>>> valid.
>>
>> When the term "incomplete" is applied to formal systems in this way it
>> is a God damned lie.
>
> No, YOU are the "God Dammed Liar", because you don't speak the truth,
> because it seems you don't actually KNOW the Truth.
>
> Definitions are what they are.
>
> Unless you have been lying about your health, you will likely find this
> out at some point soon and make it empirical knowledge.
>
>>
>>>
>>> That it does't meet your INCORRECT ideas, isn't grounds to claim they
>>> are.
>>
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/11/2022 9:36 AM, Richard Damon wrote:
> On 12/11/22 7:23 AM, olcott wrote:
>> On 12/11/2022 9:15 AM, Richard Damon wrote:
>>> On 12/11/22 7:11 AM, olcott wrote:
>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>> So which one is it?
>>>>>
>>>>> The disjunction requires a valid proof.
>>>>>
>>>>
>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>
>>>
>>> Says Who? Provide a valid reference from someone knowlegable of the
>>> field.
>>>
>>> You are using the wrong definitions of the terms.
>>
>>
>> When everyone else uses to terms incorrectly then I seem like the black
>> sheep of a herd of sheep. The sheep never notice their own group-think
>> error. https://www.psychologytoday.com/us/basics/groupthink
>>
>> Truth itself is not a Democracy. Prior to Pythagoras there was a
>> universal consensus that the Earth was flat. This does not make the
>> Earth flat it merely means that everyone was wrong.
>>
>
> Right, EMPIRICAL truth is established outside of agreement, but based on
> what is.
>
> But, Theorems do not operate on the physical universe, but the agreed
> upon universe of agreed logic. There is a difference by Logic Theories,
> and Scientific Hypothosis/Theory.

Agreeing on an incoherent set of definitions on the basis of not
noticing the incoherence does not eliminate this incoherence.

>
> IF everyone else uses a term one way, in a system based on agreement,
> and one person uses it diffrerently, that one is BY DEFINITION, incorrect.
>
> You seem to still have a fundamental lack of understanding of that which
> you are talking about.

Everyone rebutting my claims does so only by making sure to ignore the
incoherence of the foundation of the received view. They do this because
they only "know" these things on basis of learned-by-rote dogma and
never begin to carefully examine the semantic foundations of this dogma.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/11/22 7:49 AM, olcott wrote:
> On 12/11/2022 9:36 AM, Richard Damon wrote:
>> On 12/11/22 7:23 AM, olcott wrote:
>>> On 12/11/2022 9:15 AM, Richard Damon wrote:
>>>> On 12/11/22 7:11 AM, olcott wrote:
>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>> So which one is it?
>>>>>>
>>>>>> The disjunction requires a valid proof.
>>>>>>
>>>>>
>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>>
>>>>
>>>> Says Who? Provide a valid reference from someone knowlegable of the
>>>> field.
>>>>
>>>> You are using the wrong definitions of the terms.
>>>
>>>
>>> When everyone else uses to terms incorrectly then I seem like the black
>>> sheep of a herd of sheep. The sheep never notice their own group-think
>>> error. https://www.psychologytoday.com/us/basics/groupthink
>>>
>>> Truth itself is not a Democracy. Prior to Pythagoras there was a
>>> universal consensus that the Earth was flat. This does not make the
>>> Earth flat it merely means that everyone was wrong.
>>>
>>
>> Right, EMPIRICAL truth is established outside of agreement, but based
>> on what is.
>>
>> But, Theorems do not operate on the physical universe, but the agreed
>> upon universe of agreed logic. There is a difference by Logic
>> Theories, and Scientific Hypothosis/Theory.
>
> Agreeing on an incoherent set of definitions on the basis of not
> noticing the incoherence does not eliminate this incoherence.

So, can you actually PROVE the incoherence?

Everything you have done is based on adding an INCORRECT axiom to the
system.

YOUR system is incoherent because it doesn't understand what it is
talking about.

You don't even seem to understand what it means to PROVE something.

>
>>
>> IF everyone else uses a term one way, in a system based on agreement,
>> and one person uses it diffrerently, that one is BY DEFINITION,
>> incorrect.
>>
>> You seem to still have a fundamental lack of understanding of that
>> which you are talking about.
>
> Everyone rebutting my claims does so only by making sure to ignore the
> incoherence of the foundation of the received view. They do this because
> they only "know" these things on basis of learned-by-rote dogma and
> never begin to carefully examine the semantic foundations of this dogma.
>

But they aren't incoherent. Only YOU think they are, because, as you
have made know, you haven't actually studied what they mean.

You are just proving your stupidity.

I don't think you actually know what "incoherent" means.

On 12/11/22 7:43 AM, olcott wrote:
> On 12/11/2022 9:24 AM, Richard Damon wrote:
>> On 12/11/22 7:17 AM, olcott wrote:
>>> On 12/11/2022 9:08 AM, Richard Damon wrote:
>>>> On 12/11/22 5:53 AM, olcott wrote:
>>>>> On 12/10/2022 10:19 PM, Richard Damon wrote:
>>>>>> On 12/10/22 6:33 PM, olcott wrote:
>>>>>>> On 12/10/2022 8:18 PM, Richard Damon wrote:
>>>>>>>> On 12/10/22 5:59 PM, olcott wrote:
>>>>>>>>> Theorem 1.
>>>>>>>>> Every valid logical expression is provable. Equivalently, every
>>>>>>>>> logical expression is either satisfiable or refutable.
>>>>>>>>> https://plato.stanford.edu/entries/goedel/#ComThe
>>>>>>>>>
>>>>>>>>> The conventional definition of incompleteness:
>>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>
>>>>>>>>> Should actually be written as:
>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>> thus abolishing Incompleteness.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Did you notice what domain that Theorem was stated for?
>>>>>>>>
>>>>>>>> "First Order" deals with just a small limited subset of
>>>>>>>> Mathematics.
>>>>>>>>
>>>>>>>> Yes, it is know that First Orders system can be complete, but
>>>>>>>> can not express all the known properties of the Natural Numbers.
>>>>>>>>
>>>>>>>> Comutation Theory is NOT a "First Order Predicate Calculus" (it
>>>>>>>> uses Higher Order logical predicated), so that Theorem doesn't
>>>>>>>> apply.
>>>>>>>
>>>>>>> None-the-less its still applies to the philosophical foundation
>>>>>>> of every
>>>>>>> formal system. If an expression of formal or natural language is
>>>>>>> neither
>>>>>>> provable nor refutable then it is not a logical expression of any
>>>>>>> kind
>>>>>>> at all.
>>>>>>>
>>>>>>
>>>>>> Nope. Shows you don't understand what you are talking about,
>>>>>>
>>>>>> Note, it isn't that True is DEFINED as provable, but that for many
>>>>>> first order systems, it can be proven that all true statements can
>>>>>> be proven.
>>>>>>
>>>>>> Yes, it is possible to include in a system an Axiom/Definition
>>>>>> that says that all True Statements are Provable, and such a system
>>>>>> needs to limit its logical capability, like it can only use first
>>>>>> order predicates, or it will become inconsistent, and such
>>>>>> inconsistancy might not be detectable within the system.
>>>>>>
>>>>>> Such a system can NOT handle the fullness of Mathematics, or
>>>>>> systems like Computation Theory
>>>>>>
>>>>>
>>>>> It handles the subset of computations that are decision problems
>>>>> through the Curry Howard Isomorphism.
>>>>
>>>> No, Computation Theory uses logic operations not allowed
>>>> withinvsystems that meet the requirements of the Completeness Theorem.
>>>>
>>>> Curry Howard also only applies in systems that HAVE programs, which
>>>> aren't the sort of systems that the Completeness Theorem holds for.
>>>>
>>>> You are just showing you don't understand the concept of
>>>> pre-requirements of a Theory.
>>>>
>>>
>>> Every expression of language that cannot possibly resolve to true or
>>> false is not a logic expression. The computation deriving the square
>>> foot area of a house is not a logic expression.
>>>
>>>>>
>>>>>>> Everyone that has been debating me on this forum does so entirely
>>>>>>> on the
>>>>>>> basis of learn-by-rote dogma.
>>>>>>
>>>>>> Nope, you have been arguing from never-learned-due-to-stupdity dogma.
>>>>>>
>>>>>> Your IGNORANCE does make your statements true.
>>>>>>
>>>>>>>
>>>>>>> No one has considered that this math dogma might be inconsistent
>>>>>>> thus
>>>>>>> incoherent when examined through its foundation basis.
>>>>>>>
>>>>>>
>>>>>> No, you are just showing that you don't understanf what you are
>>>>>> talking about.
>>>>>
>>>>> The conventional definition of incompleteness:
>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>
>>>>> is wrong the correct way to say this is
>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>
>>>>
>>>> No, your "Valid" is just a restatement of Complete.
>>>>
>>>
>>> You are ignoring GIGO: garbage in, garbage out.
>>> Every self-contradictory expression of language that previously
>>> showed that a formal system is incomplete actually shows that the
>>> expression itself is garbage.
>>
>> No, YOU are talking GIGO since the expresions that you are refering to
>> are NOT "Self-contradictory".
>>
>> The statement that "Statement X is not provable" is NOT a
>> self-contradictory statement.
>
>
>    We are therefore confronted with a proposition which asserts
>    its own unprovability. (page 40/43)
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>
> X := "Statement X is not provable"

No, that isn't the statement. The x := isn't part of the statement, but
is just an emperical fact from the system.

You are just showing you don't understand what you are talking about and
working off the "cliff notes" version, and thinking it is giving you all
the details.

>
>>
>>>
>>>> I don't know of a use of the Valid as applying to SYSTEMS, just
>>>> arguments/proofs. The closes to Validity is Consistent, which means
>>>> that no statement can be proven both True and False.
>>>>
>>>> There is nothing "Wrong" with an incomplete system that makes is not
>>>> valid.
>>>
>>> When the term "incomplete" is applied to formal systems in this way
>>> it is a God damned lie.
>>
>> No, YOU are the "God Dammed Liar", because you don't speak the truth,
>> because it seems you don't actually KNOW the Truth.
>>
>> Definitions are what they are.
>>
>> Unless you have been lying about your health, you will likely find
>> this out at some point soon and make it empirical knowledge.
>>
>>>
>>>>
>>>> That it does't meet your INCORRECT ideas, isn't grounds to claim
>>>> they are.
>>>
>>
>

On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
> On 12/11/2022 9:21 AM, Skep Dick wrote:
> > On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
> >> On 12/11/2022 8:44 AM, Skep Dick wrote:
> >>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
> >>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>> So which one is it?
> >>>
> >>> The disjunction requires a valid proof.
> >>>
> >> Unless φ is provable or refutable φ is not a logic expression.
> > ERGO!!!
> >
> > 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
> >
> >
> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
> a slightly adapted FOL syntax.

Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))

the expression "1,2,3,4...n" is **NOT** a valid logic expression!

On 12/11/2022 10:39 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>> So which one is it?
>>>>>
>>>>> The disjunction requires a valid proof.
>>>>>
>>>> Unless φ is provable or refutable φ is not a logic expression.
>>> ERGO!!!
>>>
>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
>>>
>>>
>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
>> a slightly adapted FOL syntax.
>
> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>
> the expression "1,2,3,4...n" is **NOT** a valid logic expression!

Only because you did not encode it correctly: ∃n ∈ ℕ

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
> On 12/11/2022 10:39 AM, Skep Dick wrote:
> > On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
> >> On 12/11/2022 9:21 AM, Skep Dick wrote:
> >>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
> >>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
> >>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
> >>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>>>> So which one is it?
> >>>>>
> >>>>> The disjunction requires a valid proof.
> >>>>>
> >>>> Unless φ is provable or refutable φ is not a logic expression.
> >>> ERGO!!!
> >>>
> >>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
> >>>
> >>>
> >> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
> >> a slightly adapted FOL syntax.
> >
> > Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >
> > the expression "1,2,3,4...n" is **NOT** a valid logic expression!
> Only because you did not encode it correctly: ∃n ∈ ℕ
Sir.

let φ = "∃n ∈ ℕ"

Valid(∃n ∈ ℕ) ↔ ((T ⊢ (∃n ∈ ℕ)) ∨ (T ⊢ ¬(∃n ∈ ℕ)))

Which one is it, sir?

On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
> On 12/11/2022 10:39 AM, Skep Dick wrote:
> > On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
> >> On 12/11/2022 9:21 AM, Skep Dick wrote:
> >>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
> >>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
> >>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
> >>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>>>> So which one is it?
> >>>>>
> >>>>> The disjunction requires a valid proof.
> >>>>>
> >>>> Unless φ is provable or refutable φ is not a logic expression.
> >>> ERGO!!!
> >>>
> >>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
> >>>
> >>>
> >> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
> >> a slightly adapted FOL syntax.
> >
> > Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >
> > the expression "1,2,3,4...n" is **NOT** a valid logic expression!
> Only because you did not encode it correctly: ∃n ∈ ℕ

Furthermore, Sir.

https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b> where b is a proof of Q.

Sir. You can interpret <0,a> and <1, b> through the semantics of the usual Either-monad. Sir.

Where Left and Right are the usual projections: Left<a,b> ↔ a and Right<a,b> ↔ b

https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html

On 12/11/2022 11:46 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>> So which one is it?
>>>>>>>
>>>>>>> The disjunction requires a valid proof.
>>>>>>>
>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>> ERGO!!!
>>>>>
>>>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
>>>>>
>>>>>
>>>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
>>>> a slightly adapted FOL syntax.
>>>
>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>
>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>> Only because you did not encode it correctly: ∃n ∈ ℕ
>
> Furthermore, Sir.
>
> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b> where b is a proof of Q.
>
> Sir. You can interpret <0,a> and <1, b> through the semantics of the usual Either-monad. Sir.
>
> Where Left and Right are the usual projections: Left<a,b> ↔ a and Right<a,b> ↔ b
>
> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html

Is_a_Theorem_of_T(φ) 0 1 0 1
Is_a_Theorem_of_T(¬φ) 0 0 1 1
∨ 0 1 1 1

--
Copyright 2022 Olcott

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

On 12/11/2022 11:29 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>> So which one is it?
>>>>>>>
>>>>>>> The disjunction requires a valid proof.
>>>>>>>
>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>> ERGO!!!
>>>>>
>>>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
>>>>>
>>>>>
>>>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
>>>> a slightly adapted FOL syntax.
>>>
>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>
>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>> Only because you did not encode it correctly: ∃n ∈ ℕ
> Sir.
>
> let φ = "∃n ∈ ℕ"
>
> Valid(∃n ∈ ℕ) ↔ ((T ⊢ (∃n ∈ ℕ)) ∨ (T ⊢ ¬(∃n ∈ ℕ)))
>
> Which one is it, sir?

Yeah right, like you may believe that an element of ℕ might be a bowl of
dead cockroaches unless I expressly say otherwise.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
> On 12/11/2022 11:46 AM, Skep Dick wrote:
> > On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
> >> On 12/11/2022 10:39 AM, Skep Dick wrote:
> >>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
> >>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
> >>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
> >>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
> >>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
> >>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>>>>>> So which one is it?
> >>>>>>>
> >>>>>>> The disjunction requires a valid proof.
> >>>>>>>
> >>>>>> Unless φ is provable or refutable φ is not a logic expression.
> >>>>> ERGO!!!
> >>>>>
> >>>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
> >>>>>
> >>>>>
> >>>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
> >>>> a slightly adapted FOL syntax.
> >>>
> >>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>>
> >>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
> >> Only because you did not encode it correctly: ∃n ∈ ℕ
> >
> > Furthermore, Sir.
> >
> > https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
> > A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b> where b is a proof of Q.
> >
> > Sir. You can interpret <0,a> and <1, b> through the semantics of the usual Either-monad. Sir.
> >
> > Where Left and Right are the usual projections: Left<a,b> ↔ a and Right<a,b> ↔ b
> >
> > https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
> Is_a_Theorem_of_T(φ) 0 1 0 1
> Is_a_Theorem_of_T(¬φ) 0 0 1 1
> ∨ 0 1 1 1
*sigh* Moron. What is confusing you about the sentence "Disjunctions require proof"?

The ∨ operator is a disjunction.. It's not enough to tell us that P or Q is a theorem. That claim is incomplete.

In order to complete the claim you need to provide us with the additional information telling us **which one** (P or Q) holds!

On Sunday, 11 December 2022 at 21:20:31 UTC+2, olcott wrote:
> Yeah right, like you may believe that an element of ℕ might be a bowl of
> dead cockroaches unless I expressly say otherwise.
Well, YOU are the idiot who stated it as a disjunction.

So tell us which implication holds: T ⊢ (∃n ∈ ℕ) ∨ T ⊢ ¬(∃n ∈ ℕ)

Left or Right.

On 12/11/2022 1:29 PM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>> So which one is it?
>>>>>>>>>
>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>
>>>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>>>> ERGO!!!
>>>>>>>
>>>>>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
>>>>>>>
>>>>>>>
>>>>>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
>>>>>> a slightly adapted FOL syntax.
>>>>>
>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>
>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>
>>> Furthermore, Sir.
>>>
>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b> where b is a proof of Q.
>>>
>>> Sir. You can interpret <0,a> and <1, b> through the semantics of the usual Either-monad. Sir.
>>>
>>> Where Left and Right are the usual projections: Left<a,b> ↔ a and Right<a,b> ↔ b
>>>
>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>> Is_a_Theorem_of_T(φ) 0 1 0 1
>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>> ∨ 0 1 1 1
> *sigh* Moron. What is confusing you about the sentence "Disjunctions require proof"?
>
> The ∨ operator is a disjunction.. It's not enough to tell us that P or Q is a theorem. That claim is incomplete.
>
> In order to complete the claim you need to provide us with the additional information telling us **which one** (P or Q) holds!
>
>

The truth table already has the fully semantics of all of that and you
know this thus are only playing deceptive head games.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
> Only because you did not encode it correctly: ∃n ∈ ℕ
One more time for the slow kid in the room...

Imagine a conversation between a classical mathematician and an intuitionist, say a woman and a man respectively. She speaks first:
Her:I have just proved ∃xA.
Him: Congratulations! What is it?
Her: I don’t know. I assumed ∀x¬A and derived a contradiction.
Him: Oh. You proved ¬∀x¬A.
Her: That’s what I said.

Or another:

Her: I have proved A ∨ B.
Him: Good. Which did you prove?
Her: What?
Him: You said you proved A or B; which did you prove?
Her: Neither; I assumed ¬A & ¬B and derived a contradiction.
Him: Oh, you proved ¬[¬A & ¬B].
Her: That’s right. It’s another way of putting the same thing

Read this paper to better understand intuitionism: https://web.math.princeton.edu/~nelson/papers/int.pdf

On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
> On 12/11/2022 1:29 PM, Skep Dick wrote:
> > On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
> >> On 12/11/2022 11:46 AM, Skep Dick wrote:
> >>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
> >>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
> >>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
> >>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
> >>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
> >>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
> >>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
> >>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>>>>>>>> So which one is it?
> >>>>>>>>>
> >>>>>>>>> The disjunction requires a valid proof.
> >>>>>>>>>
> >>>>>>>> Unless φ is provable or refutable φ is not a logic expression.
> >>>>>>> ERGO!!!
> >>>>>>>
> >>>>>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
> >>>>>>>
> >>>>>>>
> >>>>>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
> >>>>>> a slightly adapted FOL syntax.
> >>>>>
> >>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >>>>>
> >>>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
> >>>> Only because you did not encode it correctly: ∃n ∈ ℕ
> >>>
> >>> Furthermore, Sir.
> >>>
> >>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
> >>> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b> where b is a proof of Q.
> >>>
> >>> Sir. You can interpret <0,a> and <1, b> through the semantics of the usual Either-monad. Sir.
> >>>
> >>> Where Left and Right are the usual projections: Left<a,b> ↔ a and Right<a,b> ↔ b
> >>>
> >>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
> >> Is_a_Theorem_of_T(φ) 0 1 0 1
> >> Is_a_Theorem_of_T(¬φ) 0 0 1 1
> >> ∨ 0 1 1 1
> > *sigh* Moron. What is confusing you about the sentence "Disjunctions require proof"?
> >
> > The ∨ operator is a disjunction.. It's not enough to tell us that P or Q is a theorem. That claim is incomplete.
> >
> > In order to complete the claim you need to provide us with the additional information telling us **which one** (P or Q) holds!
> >
> >
> The truth table already has the fully semantics of all of that and you
> know this thus are only playing deceptive head games.
One more time for the slow kid in the room...

Imagine a conversation between a classical mathematician and an intuitionist, say a woman and a man respectively. She speaks first:
Her:I have just proved ∃xA.
Him: Congratulations! What is it?
Her: I don’t know. I assumed ∀x¬A and derived a contradiction.
Him: Oh. You proved ¬∀x¬A.
Her: That’s what I said.

Or another:

Her: I have proved A ∨ B.
Him: Good. Which did you prove?
Her: What?
Him: You said you proved A or B; which did you prove?
Her: Neither; I assumed ¬A & ¬B and derived a contradiction.
Him: Oh, you proved ¬[¬A & ¬B].
Her: That’s right. It’s another way of putting the same thing

But he does not agree with her last statement; they have a different
semantics and a different notion of proof. This paper is an attempt to
understand the differences between them.

Read this paper to better understand intuitionism: https://web.math.princeton.edu/~nelson/papers/int.pdf

On 12/11/2022 1:45 PM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
>> On 12/11/2022 1:29 PM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>>>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>> So which one is it?
>>>>>>>>>>>
>>>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>>>
>>>>>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>>>>>> ERGO!!!
>>>>>>>>>
>>>>>>>>> 1 to n is NOT a logic expression. Because logic expressiong (e.g the sort of things you are referring to when you say "φ") DON'T contain free variables.
>>>>>>>>>
>>>>>>>>>
>>>>>>>> Using my MTT one can construct an 1,2,3,4...n ary logic expression using
>>>>>>>> a slightly adapted FOL syntax.
>>>>>>>
>>>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>
>>>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>>>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>>>
>>>>> Furthermore, Sir.
>>>>>
>>>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>>>> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b> where b is a proof of Q.
>>>>>
>>>>> Sir. You can interpret <0,a> and <1, b> through the semantics of the usual Either-monad. Sir.
>>>>>
>>>>> Where Left and Right are the usual projections: Left<a,b> ↔ a and Right<a,b> ↔ b
>>>>>
>>>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>>>> Is_a_Theorem_of_T(φ) 0 1 0 1
>>>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>>>> ∨ 0 1 1 1
>>> *sigh* Moron. What is confusing you about the sentence "Disjunctions require proof"?
>>>
>>> The ∨ operator is a disjunction.. It's not enough to tell us that P or Q is a theorem. That claim is incomplete.
>>>
>>> In order to complete the claim you need to provide us with the additional information telling us **which one** (P or Q) holds!
>>>
>>>
>> The truth table already has the fully semantics of all of that and you
>> know this thus are only playing deceptive head games.
> One more time for the slow kid in the room...
>

I am establishing the epistemological foundation inheritance hierarchy
(upper ontology) of analytical truth itself. Every logic system must be
derived from this foundation or it is incorrect by definition.

(1) Expressions of (formal or natural) language that are stipulated to
have the semantic value of Boolean true. Same idea as Haskell Curry
elementary theorems or natural language verified facts.
https://www.liarparadox.org/Haskell_Curry_45.pdf

(2) Expressions derived by applying truth preserving operations to (1)
or the output of (2).

In information science, an upper ontology (also known as a top-level
ontology, upper model, or foundation ontology) is an ontology (in the
sense used in information science) which consists of very general terms
(such as "object", "property", "relation") that are common across all
domains. An important function of an upper ontology is to support broad
semantic interoperability among a large number of domain-specific
ontologies by providing a common starting point for the formulation of
definitions. https://en.wikipedia.org/wiki/Upper_ontology

The rest of what you say is totally extraneous to this.

> Imagine a conversation between a classical mathematician and an intuitionist, say a woman and a man respectively. She speaks first:
> Her:I have just proved ∃xA.
> Him: Congratulations! What is it?
> Her: I don’t know. I assumed ∀x¬A and derived a contradiction.
> Him: Oh. You proved ¬∀x¬A.
> Her: That’s what I said.
>
> Or another:
>
> Her: I have proved A ∨ B.
> Him: Good. Which did you prove?
> Her: What?
> Him: You said you proved A or B; which did you prove?
> Her: Neither; I assumed ¬A & ¬B and derived a contradiction.
> Him: Oh, you proved ¬[¬A & ¬B].
> Her: That’s right. It’s another way of putting the same thing
>
> But he does not agree with her last statement; they have a different
> semantics and a different notion of proof. This paper is an attempt to
> understand the differences between them.
>
> Read this paper to better understand intuitionism: https://web.math.princeton.edu/~nelson/papers/int.pdf
>
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Sunday, 11 December 2022 at 22:38:33 UTC+2, olcott wrote:
> I am establishing the epistemological foundation inheritance hierarchy
> (upper ontology) of analytical truth itself. Every logic system must be
> derived from this foundation or it is incorrect by definition.
🤣🤣🤣🤣🤣

Dumb foundationalist!

https://en.wikipedia.org/wiki/Anti-foundationalism

On 12/11/22 3:38 PM, olcott wrote:
> On 12/11/2022 1:45 PM, Skep Dick wrote:
>> On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
>>> On 12/11/2022 1:29 PM, Skep Dick wrote:
>>>> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>>>>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>>>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>>> So which one is it?
>>>>>>>>>>>>
>>>>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>>>>
>>>>>>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>>>>>>> ERGO!!!
>>>>>>>>>>
>>>>>>>>>> 1 to n is NOT a logic expression. Because logic expressiong
>>>>>>>>>> (e.g the sort of things you are referring to when you say "φ")
>>>>>>>>>> DON'T contain free variables.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> Using my MTT one can construct an 1,2,3,4...n ary logic
>>>>>>>>> expression using
>>>>>>>>> a slightly adapted FOL syntax.
>>>>>>>>
>>>>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>
>>>>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>>>>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>>>>
>>>>>> Furthermore, Sir.
>>>>>>
>>>>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>>>>> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b>
>>>>>> where b is a proof of Q.
>>>>>>
>>>>>> Sir. You can interpret <0,a> and <1, b> through the semantics of
>>>>>> the usual Either-monad. Sir.
>>>>>>
>>>>>> Where Left and Right are the usual projections: Left<a,b> ↔ a and
>>>>>> Right<a,b> ↔ b
>>>>>>
>>>>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>>>>> Is_a_Theorem_of_T(φ) 0 1 0 1
>>>>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>>>>> ∨ 0 1 1 1
>>>> *sigh* Moron. What is confusing you about the sentence "Disjunctions
>>>> require proof"?
>>>>
>>>> The ∨ operator is a disjunction.. It's not enough to tell us that P
>>>> or Q is a theorem. That claim is incomplete.
>>>>
>>>> In order to complete the claim you need to provide us with the
>>>> additional information telling us **which one** (P or Q) holds!
>>>>
>>>>
>>> The truth table already has the fully semantics of all of that and you
>>> know this thus are only playing deceptive head games.
>> One more time for the slow kid in the room...
>>
>
> I am establishing the epistemological foundation inheritance hierarchy
> (upper ontology) of analytical truth itself. Every logic system must be
> derived from this foundation or it is incorrect by definition.

Soure of this?

Why do things need to be based on a foundation that didn't exist when
they were founded?

Seems untruthful to me.

You don't seem to understand what Epistemology is about, it isn't about
"Truth", but "Knowledge", which are different things.

Yes, we can only KNOW something to be true by either PROVING it
(analytical Truth) or OBSERVING it (Synthetic Truth), but it can be True
but unknown.

>
> (1) Expressions of (formal or natural) language that are stipulated to
> have the semantic value of Boolean true. Same idea as Haskell Curry
> elementary theorems or natural language verified facts.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
>
> (2) Expressions derived by applying truth preserving operations to (1)
> or the output of (2).

And what in this requires that actually True statements be Provable?

>
> In information science, an upper ontology (also known as a top-level
> ontology, upper model, or foundation ontology) is an ontology (in the
> sense used in information science) which consists of very general terms
> (such as "object", "property", "relation") that are common across all
> domains. An important function of an upper ontology is to support broad
> semantic interoperability among a large number of domain-specific
> ontologies by providing a common starting point for the formulation of
> definitions.  https://en.wikipedia.org/wiki/Upper_ontology
>
> The rest of what you say is totally extraneous to this.

But ontologies are discovered, not defined.

The article you reference also points out that even the major advocates
of an "Upper Ontology" don't claim that this cover ALL aspects of the
universe, just enough to be useful.

The only entity which might have the ability to develop the actual
"Upper Ontology" of the Univerese would be God Himself (since he built
the Universe, perhaps to follow some basic principles that He decided).

Now, I seem to remember that at some point in the past you claimed to be
God himself, so this may explain why you think you can do this, but you
clearly aren't, as God Himeself would be capable of explaining it so as
to be understood.

>
>> Imagine a conversation between a classical mathematician and an
>> intuitionist, say a woman and a man respectively. She speaks first:
>> Her:I have just proved ∃xA.
>> Him: Congratulations! What is it?
>> Her: I don’t know. I assumed ∀x¬A and derived a contradiction.
>> Him: Oh. You proved ¬∀x¬A.
>> Her: That’s what I said.
>>
>> Or another:
>>
>> Her: I have proved A ∨ B.
>> Him: Good. Which did you prove?
>> Her: What?
>> Him: You said you proved A or B; which did you prove?
>> Her: Neither; I assumed ¬A & ¬B and derived a contradiction.
>> Him: Oh, you proved ¬[¬A & ¬B].
>> Her: That’s right. It’s another way of putting the same thing
>>
>> But he does not agree with her last statement; they have a different
>> semantics and a different notion of proof. This paper is an attempt to
>> understand the differences between them.
>>
>> Read this paper to better understand intuitionism:
>> https://web.math.princeton.edu/~nelson/papers/int.pdf
>>
>>
>

On 12/12/2022 6:35 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 22:38:33 UTC+2, olcott wrote:
>> I am establishing the epistemological foundation inheritance hierarchy
>> (upper ontology) of analytical truth itself. Every logic system must be
>> derived from this foundation or it is incorrect by definition.
> 🤣🤣🤣🤣🤣
>
> Dumb foundationalist!
>
> https://en.wikipedia.org/wiki/Anti-foundationalism

Freaking moron.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/12/2022 6:35 AM, Skep Dick wrote:
> On Sunday, 11 December 2022 at 22:38:33 UTC+2, olcott wrote:
>> I am establishing the epistemological foundation inheritance hierarchy
>> (upper ontology) of analytical truth itself. Every logic system must be
>> derived from this foundation or it is incorrect by definition.
> 🤣🤣🤣🤣🤣
>
> Dumb foundationalist!
>
> https://en.wikipedia.org/wiki/Anti-foundationalism

Anyone that rejects tautologies is necessarily incorrect. The entire set
of analytic truth is based on mutually self defining semantic
tautologies. You don't know what any of these words mean so disagree to
mask your willful ignorance.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/12/2022 7:05 AM, Richard Damon wrote:
> On 12/11/22 3:38 PM, olcott wrote:
>> On 12/11/2022 1:45 PM, Skep Dick wrote:
>>> On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
>>>> On 12/11/2022 1:29 PM, Skep Dick wrote:
>>>>> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>>>>>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>>>>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>>>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>>>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>>>> So which one is it?
>>>>>>>>>>>>>
>>>>>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>>>>>
>>>>>>>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>>>>>>>> ERGO!!!
>>>>>>>>>>>
>>>>>>>>>>> 1 to n is NOT a logic expression. Because logic expressiong
>>>>>>>>>>> (e.g the sort of things you are referring to when you say
>>>>>>>>>>> "φ") DON'T contain free variables.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>> Using my MTT one can construct an 1,2,3,4...n ary logic
>>>>>>>>>> expression using
>>>>>>>>>> a slightly adapted FOL syntax.
>>>>>>>>>
>>>>>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>
>>>>>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>>>>>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>>>>>
>>>>>>> Furthermore, Sir.
>>>>>>>
>>>>>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>>>>>> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b>
>>>>>>> where b is a proof of Q.
>>>>>>>
>>>>>>> Sir. You can interpret <0,a> and <1, b> through the semantics of
>>>>>>> the usual Either-monad. Sir.
>>>>>>>
>>>>>>> Where Left and Right are the usual projections: Left<a,b> ↔ a and
>>>>>>> Right<a,b> ↔ b
>>>>>>>
>>>>>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>>>>>> Is_a_Theorem_of_T(φ) 0 1 0 1
>>>>>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>>>>>> ∨ 0 1 1 1
>>>>> *sigh* Moron. What is confusing you about the sentence
>>>>> "Disjunctions require proof"?
>>>>>
>>>>> The ∨ operator is a disjunction.. It's not enough to tell us that P
>>>>> or Q is a theorem. That claim is incomplete.
>>>>>
>>>>> In order to complete the claim you need to provide us with the
>>>>> additional information telling us **which one** (P or Q) holds!
>>>>>
>>>>>
>>>> The truth table already has the fully semantics of all of that and you
>>>> know this thus are only playing deceptive head games.
>>> One more time for the slow kid in the room...
>>>
>>
>> I am establishing the epistemological foundation inheritance hierarchy
>> (upper ontology) of analytical truth itself. Every logic system must be
>> derived from this foundation or it is incorrect by definition.
>
> Soure of this?
>
> Why do things need to be based on a foundation that didn't exist when
> they were founded?
>
> Seems untruthful to me.
>
> You don't seem to understand what Epistemology is about, it isn't about
> "Truth", but "Knowledge", which are different things.
>

Not really, truth includes things that are unknown, yet the only way
that we know any analytic expressions of language are true is we
understand the semantic connections that define their meaning. The
entirely body of semantic truth is true on the basis of semantic
tautology.

> Yes, we can only KNOW something to be true by either PROVING it
> (analytical Truth) or OBSERVING it (Synthetic Truth), but it can be True
> but unknown.
>

Analytic expressions of language are verified as completely true
entirely based on their meaning. In other words they are semantic
tautologies.

True, but, unknown could only exist for analytical expressions of
language that have unknown semantic connections.

True within the body of human knowledge and unprovable within the body
of human knowledge cannot possibly exist because provable merely
verifies the semantic connections that make it true.

>>
>> (1) Expressions of (formal or natural) language that are stipulated to
>> have the semantic value of Boolean true. Same idea as Haskell Curry
>> elementary theorems or natural language verified facts.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>> (2) Expressions derived by applying truth preserving operations to (1)
>> or the output of (2).
>
> And what in this requires that actually True statements be Provable?
>
>

(1) Are proven to be true on the basis of their membership in (1).

(2) Are proven to be true by applying truth preserving operations to (1)
and/or the output of (2).

>>
>> In information science, an upper ontology (also known as a top-level
>> ontology, upper model, or foundation ontology) is an ontology (in the
>> sense used in information science) which consists of very general terms
>> (such as "object", "property", "relation") that are common across all
>> domains. An important function of an upper ontology is to support broad
>> semantic interoperability among a large number of domain-specific
>> ontologies by providing a common starting point for the formulation of
>> definitions.  https://en.wikipedia.org/wiki/Upper_ontology
>>
>> The rest of what you say is totally extraneous to this.
>
> But ontologies are discovered, not defined.

So you discovered that {cats} <are> {animals} without ever being told
the meaning of these words?

>
> The article you reference also points out that even the major advocates
> of an "Upper Ontology" don't claim that this cover ALL aspects of the
> universe, just enough to be useful.
>

It is an upper ontology thus defines the nature of truth itself.

> The only entity which might have the ability to develop the actual
> "Upper Ontology" of the Univerese would be God Himself (since he built
> the Universe, perhaps to follow some basic principles that He decided).
>

Humans can write down the elements of human knowledge in ontological
form. I had extensive discussions with Doug Lenat the founder of the
largest AI project in the world about these things.

Doug's team has spent over labor years manually creating the world's
largest ontology of common sense. It is written in CYCL a knowledge
ontology language.

> Now, I seem to remember that at some point in the past you claimed to be
> God himself, so this may explain why you think you can do this, but you
> clearly aren't, as God Himeself would be capable of explaining it so as
> to be understood.
>

I have sufficient evidence to conclude that I probably am God himself.
Only those having directly seen this evidence first-hand have a
sufficient basis to assess its merit.

I am neither all knowing nor all powerful, the conception of God that I
seem to fulfill is the Gnostic Demiurge.

If this is true then my plan would be to transform the Earth into a
paradise for all.

The bible says that God <is> Love and God <has> Wrath which is the same
nonsense as saying H2O <is> Water and H2O <has> Carbon so I reject that
God <has> Wrath as bullshit.

On 12/12/22 10:44 AM, olcott wrote:
> On 12/12/2022 7:05 AM, Richard Damon wrote:
>> On 12/11/22 3:38 PM, olcott wrote:
>>> On 12/11/2022 1:45 PM, Skep Dick wrote:
>>>> On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
>>>>> On 12/11/2022 1:29 PM, Skep Dick wrote:
>>>>>> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>>>>>>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>>>>>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>>>>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>>>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott wrote:
>>>>>>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott wrote:
>>>>>>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2, olcott wrote:
>>>>>>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>>>>> So which one is it?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> Unless φ is provable or refutable φ is not a logic expression.
>>>>>>>>>>>> ERGO!!!
>>>>>>>>>>>>
>>>>>>>>>>>> 1 to n is NOT a logic expression. Because logic expressiong
>>>>>>>>>>>> (e.g the sort of things you are referring to when you say
>>>>>>>>>>>> "φ") DON'T contain free variables.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> Using my MTT one can construct an 1,2,3,4...n ary logic
>>>>>>>>>>> expression using
>>>>>>>>>>> a slightly adapted FOL syntax.
>>>>>>>>>>
>>>>>>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>
>>>>>>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic expression!
>>>>>>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>>>>>>
>>>>>>>> Furthermore, Sir.
>>>>>>>>
>>>>>>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>>>>>>> A proof of P ∨ Q is either <0,a> where a is a proof o P or <1,b>
>>>>>>>> where b is a proof of Q.
>>>>>>>>
>>>>>>>> Sir. You can interpret <0,a> and <1, b> through the semantics of
>>>>>>>> the usual Either-monad. Sir.
>>>>>>>>
>>>>>>>> Where Left and Right are the usual projections: Left<a,b> ↔ a
>>>>>>>> and Right<a,b> ↔ b
>>>>>>>>
>>>>>>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>>>>>>> Is_a_Theorem_of_T(φ) 0 1 0 1
>>>>>>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>>>>>>> ∨ 0 1 1 1
>>>>>> *sigh* Moron. What is confusing you about the sentence
>>>>>> "Disjunctions require proof"?
>>>>>>
>>>>>> The ∨ operator is a disjunction.. It's not enough to tell us that
>>>>>> P or Q is a theorem. That claim is incomplete.
>>>>>>
>>>>>> In order to complete the claim you need to provide us with the
>>>>>> additional information telling us **which one** (P or Q) holds!
>>>>>>
>>>>>>
>>>>> The truth table already has the fully semantics of all of that and you
>>>>> know this thus are only playing deceptive head games.
>>>> One more time for the slow kid in the room...
>>>>
>>>
>>> I am establishing the epistemological foundation inheritance hierarchy
>>> (upper ontology) of analytical truth itself. Every logic system must be
>>> derived from this foundation or it is incorrect by definition.
>>
>> Soure of this?
>>
>> Why do things need to be based on a foundation that didn't exist when
>> they were founded?
>>
>> Seems untruthful to me.
>>
>> You don't seem to understand what Epistemology is about, it isn't
>> about "Truth", but "Knowledge", which are different things.
>>
>
> Not really, truth includes things that are unknown, yet the only way
> that we know any analytic expressions of language are true is we
> understand the semantic connections that define their meaning. The
> entirely body of semantic truth is true on the basis of semantic
> tautology.

Right, and since the rules of a system create a "Reality", there are
some statements that are EMPIRICALLY true that can't be analytically
proven (they require the application of an unbounded number of rules,
while an analytic proof needs a bounded number of steps).

Again, you confuse KNOWING that something is true, with it BEING true.

>
>> Yes, we can only KNOW something to be true by either PROVING it
>> (analytical Truth) or OBSERVING it (Synthetic Truth), but it can be
>> True but unknown.
>>
>
> Analytic expressions of language are verified as completely true
> entirely based on their meaning. In other words they are semantic
> tautologies.

VERIFIED, not ARE. Again, confustion of Knowledge with Truth.

>
> True, but, unknown could only exist for analytical expressions of
> language that have unknown semantic connections.

or unknowable connection, because they are at an unbound distance.

>
> True within the body of human knowledge and unprovable within the body
> of human knowledge cannot possibly exist because provable merely
> verifies the semantic connections that make it true.
>

Why does it need to be VERIFIED? Again, confusiong KNOWLEDGE with TRUTH.

You just don't seem to comprend that something are beyond the finite
nature of analytic proof, but can still be true.

>>>
>>> (1) Expressions of (formal or natural) language that are stipulated to
>>> have the semantic value of Boolean true. Same idea as Haskell Curry
>>> elementary theorems or natural language verified facts.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>> (2) Expressions derived by applying truth preserving operations to (1)
>>> or the output of (2).
>>
>> And what in this requires that actually True statements be Provable?
>>
>>
>
> (1) Are proven to be true on the basis of their membership in (1).
>
> (2) Are proven to be true by applying truth preserving operations to (1)
> and/or the output of (2).

And what says they need to be PROVEN at all?

What about things that are True because they are True.

>
>>>
>>> In information science, an upper ontology (also known as a top-level
>>> ontology, upper model, or foundation ontology) is an ontology (in the
>>> sense used in information science) which consists of very general terms
>>> (such as "object", "property", "relation") that are common across all
>>> domains. An important function of an upper ontology is to support broad
>>> semantic interoperability among a large number of domain-specific
>>> ontologies by providing a common starting point for the formulation of
>>> definitions.  https://en.wikipedia.org/wiki/Upper_ontology
>>>
>>> The rest of what you say is totally extraneous to this.
>>
>> But ontologies are discovered, not defined.
>
> So you discovered that {cats} <are> {animals} without ever being told
> the meaning of these words?

We Assign meanings to the words, and then DISCOVER that the things we
call Cats are in fact, a sub-class of the things we call animals.

Sometimes we find that our previous classification are in fact WRONG.

>
>>
>> The article you reference also points out that even the major
>> advocates of an "Upper Ontology" don't claim that this cover ALL
>> aspects of the universe, just enough to be useful.
>>
>
> It is an upper ontology thus defines the nature of truth itself.