On 12/13/22 5:31 PM, olcott wrote:

> Semantic meanings inherit their meaning from varying levels of base
> meanings. My key example of this is rejecting a set containing itself as
> semantically incoherent in that no physical or conceptual thing can
> possibly fully contain itself.
>
> Try and imagine a can of soup that totally contains itself such that it
> has no outside surfaces...
>
> Russell's paradox (and every other undecidable proposition) has never
> been anything more than semantically incoherent.
>
>

Which means your logic can't handle the infinite (even the countably
infinite).

It is easy to create a set that has a bijection to a proper subset of
itself if the set is infinite.

The fact you can't imagine this shows your mind is unable to handle
those concepts.

Simple example, the even counting numbers are a sub-set of the counting
numbers, as you can divide the counting numbers into the even counting
numbers and the odd counting numbers.

But, the even counting numbers is of the same size as the counting
numbers as you can map any counting numbrer n to and even number e by
the mapping of e = 2n.

On Tuesday, December 13, 2022 at 7:32:36 PM UTC-8, olcott wrote:
> On 12/13/2022 8:55 PM, dklei...@gmail.com wrote:
> > On Tuesday, December 13, 2022 at 2:31:57 PM UTC-8, olcott wrote:
> >> On 12/13/2022 3:49 PM, dklei...@gmail.com wrote:
> >>> On Tuesday, December 13, 2022 at 8:03:23 AM UTC-8, olcott wrote:
> >>>>
> >>>> Additional meaning postulates must be specified to distinguish never
> >>>> married from divorced. It is not that hard after one spends five years
> >>>> studying the work of Richard Montague. After one does this then one
> >>>> understands that most human general knowledge can be encoded in a single
> >>>> inheritance hierarchy tree of knowledge.
> >>>
> >>> In what way do the modifiers "inheritance hierarchy" modify the meaning of
> >>> "tree" in your system?
> >> Semantic meanings inherit their meaning from varying levels of base
> >> meanings. My key example of this is rejecting a set containing itself as
> >> semantically incoherent in that no physical or conceptual thing can
> >> possibly fully contain itself.
> >>
> >> Try and imagine a can of soup that totally contains itself such that it
> >> has no outside surfaces...
> >>
> >> Russell's paradox (and every other undecidable proposition) has never
> >> been anything more than semantically incoherent.
> >>
> > Does "inheritance hierarchy tree" have the same meaning as "tree"?
> It is a tree data structure in computer science similar to the C++
> inheritance hierarchy.
>
Wikipedia says:
"In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children, but must be connected to exactly one parent, except for the root node, which has no parent."
Is this what you mean by "inheritance hierarchy tree"?

If so what is structure of your nodes and links (connections)?

On Wednesday, 14 December 2022 at 05:48:49 UTC+2, richar...@gmail.com wrote:
> Simple example, the even counting numbers are a sub-set of the counting
> numbers, as you can divide the counting numbers into the even counting
> numbers and the odd counting numbers.
>
> But, the even counting numbers is of the same size as the counting
> numbers as you can map any counting numbrer n to and even number e by
> the mapping of e = 2n.
Eeeeeh, that's only true if you assume the usual ordering on ℕ. It's not generally true in other structures containing the same elements.

Take the infinite stream of even numbers: [0,2,4,...)
Take the infinite stream of odd numbers: [1,3,5,...)
Prefix the odd with the even such that all even numbers are <1 e.g : 0,2,4,...., 1,3,5,...

Now tell me about e=2n

On 12/14/22 1:47 AM, Skep Dick wrote:
> On Wednesday, 14 December 2022 at 05:48:49 UTC+2, richar...@gmail.com wrote:
>> Simple example, the even counting numbers are a sub-set of the counting
>> numbers, as you can divide the counting numbers into the even counting
>> numbers and the odd counting numbers.
>>
>> But, the even counting numbers is of the same size as the counting
>> numbers as you can map any counting numbrer n to and even number e by
>> the mapping of e = 2n.
> Eeeeeh, that's only true if you assume the usual ordering on ℕ. It's not generally true in other structures containing the same elements.
>
> Take the infinite stream of even numbers: [0,2,4,...)
> Take the infinite stream of odd numbers: [1,3,5,...)
> Prefix the odd with the even such that all even numbers are <1 e.g : 0,2,4,..., 1,3,5,...
>
> Now tell me about e=2n
>

First, you aren't allowed to count numbers with two ... embedded in the
sequence (at least by the classic rules, if you want to do it you need
to define the rules and show they are consistent).

And yes, they are all the "same size" because you can make the bijection
between them, even though "logic" seems to say that one is bigger than
another.

The fact that a proper subset of a set, which meets the requirements of
being "within" the full set, ends up being just as large as the full
set, is what shows that the whole can be a subset of itself.

It is a classical fact that infinity breaks a number of "obvious"
properties. This is one reason the Number System like the Naturals, and
the Reals don't include infinity as a normal "value", but just a limit
that things approach, but the sets with it included are considered to be
a DIFFERENT number system. The adding of infinity needs some careful
extra definition and the lose of some classical properties that no
longer hold.

On Wednesday, 14 December 2022 at 14:24:00 UTC+2, richar...@gmail.com wrote:
> First, you aren't allowed to count numbers with two ... embedded in the
> sequence (at least by the classic rules, if you want to do it you need
> to define the rules and show they are consistent).
Says who?

The expression [1,3..] in Haskell produces precisely ALL odd numbers in ℕ
The expression [0,2..] in Haskell produces precisely ALL even numbers in ℕ.

[0,2..] ∪ [1,3..] ↔ ℕ

If ℕ is countable, then [0,2..] ∪ [1,3..] is countable. That's how logical deduction works, right?

> The fact that a proper subset of a set, which meets the requirements of
> being "within" the full set, ends up being just as large as the full
> set, is what shows that the whole can be a subset of itself.
"Part of the whole is as big as the whole" sure sounds crazy in English.

On Wednesday, 14 December 2022 at 14:24:00 UTC+2, richar...@gmail.com wrote:
> And yes, they are all the "same size" because you can make the bijection
> between them, even though "logic" seems to say that one is bigger than
> another.
In other news...

[0,2..] ∪ [1,3..] ↔ ℕ

SIZE([0,2..]) + SIZE([1,3..]) = SIZE(ℕ)
SIZE([0,2..]) = SIZE([1,3..])
SIZE([0,2..]) = SIZE(ℕ)
SIZE([1,3..]) = SIZE(ℕ)

Houston, we have a problem!

On Wednesday, December 14, 2022 at 8:24:00 PM UTC+8, richar...@gmail.com wrote:
> On 12/14/22 1:47 AM, Skep Dick wrote:
> > On Wednesday, 14 December 2022 at 05:48:49 UTC+2, richar...@gmail.com wrote:
> >> Simple example, the even counting numbers are a sub-set of the counting
> >> numbers, as you can divide the counting numbers into the even counting
> >> numbers and the odd counting numbers.
> >>
> >> But, the even counting numbers is of the same size as the counting
> >> numbers as you can map any counting numbrer n to and even number e by
> >> the mapping of e = 2n.
> > Eeeeeh, that's only true if you assume the usual ordering on ℕ. It's not generally true in other structures containing the same elements.
> >
> > Take the infinite stream of even numbers: [0,2,4,...)
> > Take the infinite stream of odd numbers: [1,3,5,...)
> > Prefix the odd with the even such that all even numbers are <1 e.g : 0,2,4,..., 1,3,5,...
> >
> > Now tell me about e=2n
> >
> First, you aren't allowed to count numbers with two ... embedded in the
> sequence (at least by the classic rules, if you want to do it you need
> to define the rules and show they are consistent).
>
> And yes, they are all the "same size" because you can make the bijection
> between them, even though "logic" seems to say that one is bigger than
> another.
What does "same size" mean? If the 'size' cannot add, subtract, ....
olcott is partly correct that "Everyone that has been debating me on this forum
does so entirely on the basis of learn-by-rote dogma."
You just recite and think as the text-book tells what to say and how to think.
I don't think you really understand what you say (esp. those big words and logic).

> The fact that a proper subset of a set, which meets the requirements of
> being "within" the full set, ends up being just as large as the full
> set, is what shows that the whole can be a subset of itself.
>
> It is a classical fact that infinity breaks a number of "obvious"
> properties. This is one reason the Number System like the Naturals, and
> the Reals don't include infinity as a normal "value", but just a limit
> that things approach, but the sets with it included are considered to be
> a DIFFERENT number system. The adding of infinity needs some careful
> extra definition and the lose of some classical properties that no
> longer hold.

On Sunday, December 11, 2022 at 9:59:47 AM UTC+8, 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.
Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
<=> Valid(φ) ↔ TRUE

Valid(φ) is a tautology.
This explains why you think your H is correct.

On 12/14/2022 12:10 AM, dklei...@gmail.com wrote:
> On Tuesday, December 13, 2022 at 7:32:36 PM UTC-8, olcott wrote:
>> On 12/13/2022 8:55 PM, dklei...@gmail.com wrote:
>>> On Tuesday, December 13, 2022 at 2:31:57 PM UTC-8, olcott wrote:
>>>> On 12/13/2022 3:49 PM, dklei...@gmail.com wrote:
>>>>> On Tuesday, December 13, 2022 at 8:03:23 AM UTC-8, olcott wrote:
>>>>>>
>>>>>> Additional meaning postulates must be specified to distinguish never
>>>>>> married from divorced. It is not that hard after one spends five years
>>>>>> studying the work of Richard Montague. After one does this then one
>>>>>> understands that most human general knowledge can be encoded in a single
>>>>>> inheritance hierarchy tree of knowledge.
>>>>>
>>>>> In what way do the modifiers "inheritance hierarchy" modify the meaning of
>>>>> "tree" in your system?
>>>> Semantic meanings inherit their meaning from varying levels of base
>>>> meanings. My key example of this is rejecting a set containing itself as
>>>> semantically incoherent in that no physical or conceptual thing can
>>>> possibly fully contain itself.
>>>>
>>>> Try and imagine a can of soup that totally contains itself such that it
>>>> has no outside surfaces...
>>>>
>>>> Russell's paradox (and every other undecidable proposition) has never
>>>> been anything more than semantically incoherent.
>>>>
>>> Does "inheritance hierarchy tree" have the same meaning as "tree"?
>> It is a tree data structure in computer science similar to the C++
>> inheritance hierarchy.
>>
> Wikipedia says:
> "In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children, but must be connected to exactly one parent, except for the root node, which has no parent."
> Is this what you mean by "inheritance hierarchy tree"?
>
> If so what is structure of your nodes and links (connections)?

I never thought this through before, thanks.

struct
{ char GUID[32]; // The name of a unique concept
uint64_t parent;
std::vector<uint64_t> children; // might not be needed
}

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

On 12/14/2022 8:18 AM, wij wrote:
> On Wednesday, December 14, 2022 at 8:24:00 PM UTC+8, richar...@gmail.com wrote:
>> On 12/14/22 1:47 AM, Skep Dick wrote:
>>> On Wednesday, 14 December 2022 at 05:48:49 UTC+2, richar...@gmail.com wrote:
>>>> Simple example, the even counting numbers are a sub-set of the counting
>>>> numbers, as you can divide the counting numbers into the even counting
>>>> numbers and the odd counting numbers.
>>>>
>>>> But, the even counting numbers is of the same size as the counting
>>>> numbers as you can map any counting numbrer n to and even number e by
>>>> the mapping of e = 2n.
>>> Eeeeeh, that's only true if you assume the usual ordering on ℕ. It's not generally true in other structures containing the same elements.
>>>
>>> Take the infinite stream of even numbers: [0,2,4,...)
>>> Take the infinite stream of odd numbers: [1,3,5,...)
>>> Prefix the odd with the even such that all even numbers are <1 e.g : 0,2,4,..., 1,3,5,...
>>>
>>> Now tell me about e=2n
>>>
>> First, you aren't allowed to count numbers with two ... embedded in the
>> sequence (at least by the classic rules, if you want to do it you need
>> to define the rules and show they are consistent).
>>
>> And yes, they are all the "same size" because you can make the bijection
>> between them, even though "logic" seems to say that one is bigger than
>> another.
>
> What does "same size" mean? If the 'size' cannot add, subtract, ....
> olcott is partly correct that "Everyone that has been debating me on this forum
> does so entirely on the basis of learn-by-rote dogma."
> You just recite and think as the text-book tells what to say and how to think.
> I don't think you really understand what you say (esp. those big words and logic).
>

Yes, the philosophical foundation of mathematics and logic is derived
from the philosophical foundation of analytic truth and are arranged in
an inheritance hierarchy knowledge ontology such that math and logic
inherit these two properties:

(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). AKA provability

Every element of the set of analytic knowledge is established as a
semantic tautology. This converts all undecidable propositions into
semantically incorrect expressions of language.

>> The fact that a proper subset of a set, which meets the requirements of
>> being "within" the full set, ends up being just as large as the full
>> set, is what shows that the whole can be a subset of itself.
>>
>> It is a classical fact that infinity breaks a number of "obvious"
>> properties. This is one reason the Number System like the Naturals, and
>> the Reals don't include infinity as a normal "value", but just a limit
>> that things approach, but the sets with it included are considered to be
>> a DIFFERENT number system. The adding of infinity needs some careful
>> extra definition and the lose of some classical properties that no
>> longer hold.

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

On 12/14/2022 8:21 AM, wij wrote:
> On Sunday, December 11, 2022 at 9:59:47 AM UTC+8, 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.
>
> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> <=> Valid(φ) ↔ TRUE
>

*Correction*
True(φ) ↔ (T ⊢ φ)
¬True(φ) ↔ (T ⊬ φ)
False(φ) ↔ (T ⊢ ¬φ)

> Valid(φ) is a tautology.
> This explains why you think your H is correct.

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

On 12/13/2022 11:56 AM, Skep Dick wrote:
> On Tuesday, 13 December 2022 at 19:41:00 UTC+2, olcott wrote:
>> General knowledge is handled by one knowledge ontology, context is
>> handled by another separate discourse knowledge ontology.
> 🤣🤣🤣🤣🤣
>
> So now you have multiple ontologies?
>
> Which ontology is The One True Ontology?
>

There is a general knowledge ontology and a discourse context ontology.
The first one is like a dictionary and the second one is a conversation
using words from the dictionary.

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

On 12/13/2022 8:26 PM, Richard Damon wrote:
> On 12/13/22 9:22 AM, olcott wrote:
>> On 12/13/2022 4:51 AM, Skep Dick wrote:
>>> On Monday, 12 December 2022 at 16:52:22 UTC+2, olcott wrote:
>>>> 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.
>>>
>>> You dumb motherfucker! I am not rejecting your tautology.
>>>
>>> I am DECLARING that the negation of your tautology is ALSO a tautology!
>>>
>> All that you are doing is negating a necessarily true statement thus
>> forming A lie.
>>
>> {A square has four equal length} sides is a tautology.
>> {A square does not have four equal length sides} is a falsehood.
>>
>>> ∃x can be defined as a tautology.
>>> -∃x can also be defined as a tautology.
>>>
>>> You don't understand computation. Idiot.
>>>
>>
>> Is is an objective fact that I am a genius.
>>
>
> Then PROVE it.
>
> You seem to have proved the opposite.

If you focused on understanding what I say instead of focusing on
disputing what I say without understanding what I say you would see for
yourself.

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

On 12/13/2022 8:38 PM, Richard Damon wrote:
> On 12/13/22 10:56 AM, olcott wrote:
>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>> On 12/12/22 8:51 PM, olcott wrote:
>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>> 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).
>>>>>
>>>>
>>>> You don't seem to understand the difference between empirical
>>>> (verified with sense organs) and analytical verified based on the
>>>> meaning of expressions of language.
>>>
>>> No, YOU don't seem to understand the difference between Knowledge,
>>> Truth that has been verified, and Actual Truth.
>>>
>>
>> knowledge ⊂ truth
>
> Right, so some Truth is not part of Knowledge, and even some CAN'T be
> known (or it might get pulled into the proper sub-set), and thus some
> Truth is unprovable.
>
> You just ADMITTED that your claim that all Truth must be Provable is
> incorrect.
>

On Wednesday, 14 December 2022 at 16:21:35 UTC+2, wyni...@gmail.com wrote:
> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> <=> Valid(φ) ↔ TRUE
>
> Valid(φ) is a tautology.
> This explains why you think your H is correct.
It's only a tautology in systems in which excluded middle holds.

Otherwise it's just a partial computation. Either (T ⊢ φ) or (T ⊢ ¬φ). Which one?

It's the non-deterministic choice operator.

On 12/13/2022 8:38 PM, Richard Damon wrote:
> On 12/13/22 10:56 AM, olcott wrote:
>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>> On 12/12/22 8:51 PM, olcott wrote:
>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>> 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).
>>>>>
>>>>
>>>> You don't seem to understand the difference between empirical
>>>> (verified with sense organs) and analytical verified based on the
>>>> meaning of expressions of language.
>>>
>>> No, YOU don't seem to understand the difference between Knowledge,
>>> Truth that has been verified, and Actual Truth.
>>>
>>
>> knowledge ⊂ truth
>
> Right, so some Truth is not part of Knowledge, and even some CAN'T be
> known (or it might get pulled into the proper sub-set), and thus some
> Truth is unprovable.
>
> You just ADMITTED that your claim that all Truth must be Provable is
> incorrect.
>
>
>>
>>> You seem to think we need to be Omniscient.
>>>
>>>>
>>>>> 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.
>>>>>
>>>>
>>>> The only reason that analytic expressions are true is that they are
>>>> semantic tautologies.
>>>
>>> No. Analytic proofs can be based on the use of Emperical Facts, which
>>
>> Empirical(x) ≡ ¬Analytical(x)
>> Empirical(x) requires sense data for the sense organs.
>
> Nope, you are confusing Empirical KNOWLEDGE with Empirical TRUTH.
>
> You same old problem.
>
> You are also forgetting that "Senses" go beyond the "organs" and include
> the mind, and aids that extend our senses.

On 12/13/2022 8:38 PM, Richard Damon wrote:
> On 12/13/22 10:56 AM, olcott wrote:
>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>> On 12/12/22 8:51 PM, olcott wrote:
>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>> 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).
>>>>>
>>>>
>>>> You don't seem to understand the difference between empirical
>>>> (verified with sense organs) and analytical verified based on the
>>>> meaning of expressions of language.
>>>
>>> No, YOU don't seem to understand the difference between Knowledge,
>>> Truth that has been verified, and Actual Truth.
>>>
>>
>> knowledge ⊂ truth
>
> Right, so some Truth is not part of Knowledge, and even some CAN'T be
> known (or it might get pulled into the proper sub-set), and thus some
> Truth is unprovable.
>
> You just ADMITTED that your claim that all Truth must be Provable is
> incorrect.
>
>
>>
>>> You seem to think we need to be Omniscient.
>>>
>>>>
>>>>> 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.
>>>>>
>>>>
>>>> The only reason that analytic expressions are true is that they are
>>>> semantic tautologies.
>>>
>>> No. Analytic proofs can be based on the use of Emperical Facts, which
>>
>> Empirical(x) ≡ ¬Analytical(x)
>> Empirical(x) requires sense data for the sense organs.
>
> Nope, you are confusing Empirical KNOWLEDGE with Empirical TRUTH.
>
> You same old problem.
>
> You are also forgetting that "Senses" go beyond the "organs" and include
> the mind, and aids that extend our senses.
>
>>
>>> means they are NOT tautologies. We can analytically prove that Same
>>> is a Black Anaimal based on the Emperical Facts that Same is Black,
>>> and Sam is a Cat, and the categorical statement that Cats are Animals.
>>>
>>> Tautologies are statements that are True indpendent of Emperical
>>> Facts (true in all models). That Sam is a Black Animal is NOT a
>>> Tautology.
>>>
>>>>
>>>>>>
>>>>>> 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.
>>>>
>>>> Yes it may be the case that {cats} have always been {house bricks}
>>>> and we simply never noticed that {office buildings} are made out of
>>>> {cats}.
>>>
>>> Maybe not, but we have learned that while we used to classify all
>>> life into two Kingdoms as Animal or Plant, that there are other
>>> Kingdoms of creatures that don't really fit into either, like Fungi.
>>>
>>>>
>>>>>>
>>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Nope.
>>>>>
>>>>> Truth IS.
>>>>
>>>> non-existent until defined.
>>>> Can't exist apart from the abstraction of language.
>>>
>>> Nope, everything in the Universe was, even before language existed.
>>>
>>
>> I remember otherwise:
>> https://www.the-pete.org/indexc518.html?p=328
>> https://www.the-pete.org/indexdf01.html?p=441
>
> Really, are you admitting that these ramblings are yours?
>
> Again, if you could do that, why are you dying of cancer?
>
> You are just showing your insanity,

On 12/13/2022 8:38 PM, Richard Damon wrote:
> On 12/13/22 10:56 AM, olcott wrote:
>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>> On 12/12/22 8:51 PM, olcott wrote:
>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>> 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).
>>>>>
>>>>
>>>> You don't seem to understand the difference between empirical
>>>> (verified with sense organs) and analytical verified based on the
>>>> meaning of expressions of language.
>>>
>>> No, YOU don't seem to understand the difference between Knowledge,
>>> Truth that has been verified, and Actual Truth.
>>>
>>
>> knowledge ⊂ truth
>
> Right, so some Truth is not part of Knowledge, and even some CAN'T be
> known (or it might get pulled into the proper sub-set), and thus some
> Truth is unprovable.
>
> You just ADMITTED that your claim that all Truth must be Provable is
> incorrect.
>
>
>>
>>> You seem to think we need to be Omniscient.
>>>
>>>>
>>>>> 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.
>>>>>
>>>>
>>>> The only reason that analytic expressions are true is that they are
>>>> semantic tautologies.
>>>
>>> No. Analytic proofs can be based on the use of Emperical Facts, which
>>
>> Empirical(x) ≡ ¬Analytical(x)
>> Empirical(x) requires sense data for the sense organs.
>
> Nope, you are confusing Empirical KNOWLEDGE with Empirical TRUTH.
>
> You same old problem.
>
> You are also forgetting that "Senses" go beyond the "organs" and include
> the mind, and aids that extend our senses.
>
>>
>>> means they are NOT tautologies. We can analytically prove that Same
>>> is a Black Anaimal based on the Emperical Facts that Same is Black,
>>> and Sam is a Cat, and the categorical statement that Cats are Animals.
>>>
>>> Tautologies are statements that are True indpendent of Emperical
>>> Facts (true in all models). That Sam is a Black Animal is NOT a
>>> Tautology.
>>>
>>>>
>>>>>>
>>>>>> 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.
>>>>
>>>> Yes it may be the case that {cats} have always been {house bricks}
>>>> and we simply never noticed that {office buildings} are made out of
>>>> {cats}.
>>>
>>> Maybe not, but we have learned that while we used to classify all
>>> life into two Kingdoms as Animal or Plant, that there are other
>>> Kingdoms of creatures that don't really fit into either, like Fungi.
>>>
>>>>
>>>>>>
>>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Nope.
>>>>>
>>>>> Truth IS.
>>>>
>>>> non-existent until defined.
>>>> Can't exist apart from the abstraction of language.
>>>
>>> Nope, everything in the Universe was, even before language existed.
>>>
>>
>> I remember otherwise:
>> https://www.the-pete.org/indexc518.html?p=328
>> https://www.the-pete.org/indexdf01.html?p=441
>
> Really, are you admitting that these ramblings are yours?
>
> Again, if you could do that, why are you dying of cancer?
>
> You are just showing your insanity,
>
>>
>>> We couldn't talk about them, but they existed.
>>>
>>> Unless you are of the "Dream Universe" perversion, Reality isn't
>>> based on it being understood.
>>>
>>>>
>>>>>
>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Again, KNOWLEDGE, not TRUTH.
>>>>
>>>> For you I would agree. For everyone else knowledge is a subset of
>>>> truth.
>>>
>>> Yes, which means there is Truth that isn't Knowledge, and possible
>>> even is unknowable.
>>
>> Unless an expression of language is a semantic tautology is it not an
>> analytic expression of language.
>
> Nope, analytic expressions don't need to be a tautology.
>
> For instance, Cats and Dogs are in distinct animal groups can be a true
> analytical expression. its Truth is dependent on the implied meaning of
> some of the terms, so it is NOT a Tautology, which must be true in ALL
> models of the system.

On 12/13/2022 8:38 PM, Richard Damon wrote:
> On 12/13/22 10:56 AM, olcott wrote:
>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>> On 12/12/22 8:51 PM, olcott wrote:
>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>> 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).
>>>>>
>>>>
>>>> You don't seem to understand the difference between empirical
>>>> (verified with sense organs) and analytical verified based on the
>>>> meaning of expressions of language.
>>>
>>> No, YOU don't seem to understand the difference between Knowledge,
>>> Truth that has been verified, and Actual Truth.
>>>
>>
>> knowledge ⊂ truth
>
> Right, so some Truth is not part of Knowledge, and even some CAN'T be
> known (or it might get pulled into the proper sub-set), and thus some
> Truth is unprovable.
>
> You just ADMITTED that your claim that all Truth must be Provable is
> incorrect.
>
>
>>
>>> You seem to think we need to be Omniscient.
>>>
>>>>
>>>>> 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.
>>>>>
>>>>
>>>> The only reason that analytic expressions are true is that they are
>>>> semantic tautologies.
>>>
>>> No. Analytic proofs can be based on the use of Emperical Facts, which
>>
>> Empirical(x) ≡ ¬Analytical(x)
>> Empirical(x) requires sense data for the sense organs.
>
> Nope, you are confusing Empirical KNOWLEDGE with Empirical TRUTH.
>
> You same old problem.
>
> You are also forgetting that "Senses" go beyond the "organs" and include
> the mind, and aids that extend our senses.
>
>>
>>> means they are NOT tautologies. We can analytically prove that Same
>>> is a Black Anaimal based on the Emperical Facts that Same is Black,
>>> and Sam is a Cat, and the categorical statement that Cats are Animals.
>>>
>>> Tautologies are statements that are True indpendent of Emperical
>>> Facts (true in all models). That Sam is a Black Animal is NOT a
>>> Tautology.
>>>
>>>>
>>>>>>
>>>>>> 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.
>>>>
>>>> Yes it may be the case that {cats} have always been {house bricks}
>>>> and we simply never noticed that {office buildings} are made out of
>>>> {cats}.
>>>
>>> Maybe not, but we have learned that while we used to classify all
>>> life into two Kingdoms as Animal or Plant, that there are other
>>> Kingdoms of creatures that don't really fit into either, like Fungi.
>>>
>>>>
>>>>>>
>>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Nope.
>>>>>
>>>>> Truth IS.
>>>>
>>>> non-existent until defined.
>>>> Can't exist apart from the abstraction of language.
>>>
>>> Nope, everything in the Universe was, even before language existed.
>>>
>>
>> I remember otherwise:
>> https://www.the-pete.org/indexc518.html?p=328
>> https://www.the-pete.org/indexdf01.html?p=441
>
> Really, are you admitting that these ramblings are yours?
>
> Again, if you could do that, why are you dying of cancer?
>
> You are just showing your insanity,
>
>>
>>> We couldn't talk about them, but they existed.
>>>
>>> Unless you are of the "Dream Universe" perversion, Reality isn't
>>> based on it being understood.
>>>
>>>>
>>>>>
>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Again, KNOWLEDGE, not TRUTH.
>>>>
>>>> For you I would agree. For everyone else knowledge is a subset of
>>>> truth.
>>>
>>> Yes, which means there is Truth that isn't Knowledge, and possible
>>> even is unknowable.
>>
>> Unless an expression of language is a semantic tautology is it not an
>> analytic expression of language.
>
> Nope, analytic expressions don't need to be a tautology.
>
> For instance, Cats and Dogs are in distinct animal groups can be a true
> analytical expression. its Truth is dependent on the implied meaning of
> some of the terms, so it is NOT a Tautology, which must be true in ALL
> models of the system.
>
>>
>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>> If this requires counting all the way to infinity to verify then it is
>> not a tautology. If it is possible to verify in finite time then it is a
>> tautology.
>>
>
> So, your definition of an analytical expression says there are
> expression that you can't tell if they ARE analytical expressions, and
> thus you don't know if you can talk about them?
>
> Seems like A pretty weak system.
Every expression of language that does not require any sense data from
the sense organs to verify that it is true is an analytic expression of
language. That you are stuck in rebuttal mode is a form of dishonesty.

On 12/13/2022 8:38 PM, Richard Damon wrote:
> On 12/13/22 10:56 AM, olcott wrote:
>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>> On 12/12/22 8:51 PM, olcott wrote:
>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>> 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).
>>>>>
>>>>
>>>> You don't seem to understand the difference between empirical
>>>> (verified with sense organs) and analytical verified based on the
>>>> meaning of expressions of language.
>>>
>>> No, YOU don't seem to understand the difference between Knowledge,
>>> Truth that has been verified, and Actual Truth.
>>>
>>
>> knowledge ⊂ truth
>
> Right, so some Truth is not part of Knowledge, and even some CAN'T be
> known (or it might get pulled into the proper sub-set), and thus some
> Truth is unprovable.
>
> You just ADMITTED that your claim that all Truth must be Provable is
> incorrect.
>
>
>>
>>> You seem to think we need to be Omniscient.
>>>
>>>>
>>>>> 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.
>>>>>
>>>>
>>>> The only reason that analytic expressions are true is that they are
>>>> semantic tautologies.
>>>
>>> No. Analytic proofs can be based on the use of Emperical Facts, which
>>
>> Empirical(x) ≡ ¬Analytical(x)
>> Empirical(x) requires sense data for the sense organs.
>
> Nope, you are confusing Empirical KNOWLEDGE with Empirical TRUTH.
>
> You same old problem.
>
> You are also forgetting that "Senses" go beyond the "organs" and include
> the mind, and aids that extend our senses.
>
>>
>>> means they are NOT tautologies. We can analytically prove that Same
>>> is a Black Anaimal based on the Emperical Facts that Same is Black,
>>> and Sam is a Cat, and the categorical statement that Cats are Animals.
>>>
>>> Tautologies are statements that are True indpendent of Emperical
>>> Facts (true in all models). That Sam is a Black Animal is NOT a
>>> Tautology.
>>>
>>>>
>>>>>>
>>>>>> 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.
>>>>
>>>> Yes it may be the case that {cats} have always been {house bricks}
>>>> and we simply never noticed that {office buildings} are made out of
>>>> {cats}.
>>>
>>> Maybe not, but we have learned that while we used to classify all
>>> life into two Kingdoms as Animal or Plant, that there are other
>>> Kingdoms of creatures that don't really fit into either, like Fungi.
>>>
>>>>
>>>>>>
>>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Nope.
>>>>>
>>>>> Truth IS.
>>>>
>>>> non-existent until defined.
>>>> Can't exist apart from the abstraction of language.
>>>
>>> Nope, everything in the Universe was, even before language existed.
>>>
>>
>> I remember otherwise:
>> https://www.the-pete.org/indexc518.html?p=328
>> https://www.the-pete.org/indexdf01.html?p=441
>
> Really, are you admitting that these ramblings are yours?
>
> Again, if you could do that, why are you dying of cancer?
>
> You are just showing your insanity,
>
>>
>>> We couldn't talk about them, but they existed.
>>>
>>> Unless you are of the "Dream Universe" perversion, Reality isn't
>>> based on it being understood.
>>>
>>>>
>>>>>
>>>>>>
>>>>>>> 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.
>>>>>
>>>>> Again, KNOWLEDGE, not TRUTH.
>>>>
>>>> For you I would agree. For everyone else knowledge is a subset of
>>>> truth.
>>>
>>> Yes, which means there is Truth that isn't Knowledge, and possible
>>> even is unknowable.
>>
>> Unless an expression of language is a semantic tautology is it not an
>> analytic expression of language.
>
> Nope, analytic expressions don't need to be a tautology.
>
> For instance, Cats and Dogs are in distinct animal groups can be a true
> analytical expression. its Truth is dependent on the implied meaning of
> some of the terms, so it is NOT a Tautology, which must be true in ALL
> models of the system.
>
>>
>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>> If this requires counting all the way to infinity to verify then it is
>> not a tautology. If it is possible to verify in finite time then it is a
>> tautology.
>>
>
> So, your definition of an analytical expression says there are
> expression that you can't tell if they ARE analytical expressions, and
> thus you don't know if you can talk about them?
>
> Seems like A pretty weak system.
>
>>>>
>>>>>
>>>>> We might be able to catalog what we know, but not everything that
>>>>> is actually TRUE.
>>>>>
>>>>
>>>> This is enough to create a human mind using software.
>>>
>>> So, are you saying Truth is limited to what the mind can understand?
>>
>> I am saying the the sum total of all human knowledge is necessarily
>> sufficient to create a fully functional human mind. Since most all of
>> this knowledge can be organized as a tree almost all of human reasoning
>> is one kind of tree walk (DFS, BFS...) or another.
>
> Nope, just because you know everything that a person knows, doesn't mean
> you understand the rules they use to think with.
>
>>
>>>>
>>>>> Th9is seems to be an inherent flaw in your thinking.
>>>>>
>>>>>>
>>>>>> 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.
>>>>>
>>>>>
>>>>> Then you aren't God, and don't know the meaning of the word.
>>>>
>>>> That is merely your presumption.
>>>
>>> Prove me wrong.
>>
>> You are an aspect of me thus already know this is true.
>> You disagree to keep up the ruse that I am not all alone in the universe.
>
> Then are you an aspect of me too? That mean you know that you are just
> lying.
>
> You disagree because you don't understand the actual meaning of Truth.

On 12/14/2022 9:24 AM, Skep Dick wrote:
> On Wednesday, 14 December 2022 at 16:21:35 UTC+2, wyni...@gmail.com wrote:
>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>> <=> Valid(φ) ↔ TRUE
>>
>> Valid(φ) is a tautology.
>> This explains why you think your H is correct.
> It's only a tautology in systems in which excluded middle holds.
>

All expressions of formal or natural language are
(a) True
(b) False
(c) Not a truth bearer

Anyone that disagrees is necessarily incorrect.

> Otherwise it's just a partial computation. Either (T ⊢ φ) or (T ⊢ ¬φ). Which one?
>
> It's the non-deterministic choice operator.

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

On 2022-12-14 08:22, olcott wrote:

> Every undecidable proposition is merely semantically incoherent and
> nothing more. Every truth is provable including truth where one or more
> of the steps of the proof are currently unknown.

So how are you supposed to determine whether a proposition is
'incoherent' or whether it is a provable proposition whose proof is
currently unknown?

Unless you have some way of making that determination, your idea of
'incoherent' propositions isn't terribly useful.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

On Wednesday, 14 December 2022 at 18:06:22 UTC+2, olcott wrote:
> On 12/14/2022 9:24 AM, Skep Dick wrote:
> > On Wednesday, 14 December 2022 at 16:21:35 UTC+2, wyni...@gmail.com wrote:
> >> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> >> <=> Valid(φ) ↔ TRUE
> >>
> >> Valid(φ) is a tautology.
> >> This explains why you think your H is correct.
> > It's only a tautology in systems in which excluded middle holds.
> >
> All expressions of formal or natural language are
> (a) True
> (b) False
> (c) Not a truth bearer
Lets try that again...

(a) Truth-bearer
1. True
2. False
(b) Not a truth bearer
(c) As yet undetermined whether (a); or (b)

On 12/14/2022 10:59 AM, André G. Isaak wrote:
> On 2022-12-14 08:22, olcott wrote:
>
>> Every undecidable proposition is merely semantically incoherent and
>> nothing more. Every truth is provable including truth where one or
>> more of the steps of the proof are currently unknown.
>
> So how are you supposed to determine whether a proposition is
> 'incoherent' or whether it is a provable proposition whose proof is
> currently unknown?
>
> Unless you have some way of making that determination, your idea of
> 'incoherent' propositions isn't terribly useful.
>
> André
>

Although it is dead obvious that the Liar Paradox:
"This sentence is not true."
Is not a truth bearer because it is self-contradictory...

It remains the received view that the notion of truth cannot be
formalized because Tarski could not prove that the Liar Paradox is true.

Valid(T,φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
True(T,φ) ↔ ((T ⊢ φ)
¬True(T,φ) ↔ ((T ⊬ φ)
False(T,φ) ↔ ((T ⊢ ¬φ)

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

On 12/14/2022 11:02 AM, Skep Dick wrote:
> On Wednesday, 14 December 2022 at 18:06:22 UTC+2, olcott wrote:
>> On 12/14/2022 9:24 AM, Skep Dick wrote:
>>> On Wednesday, 14 December 2022 at 16:21:35 UTC+2, wyni...@gmail.com wrote:
>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>> <=> Valid(φ) ↔ TRUE
>>>>
>>>> Valid(φ) is a tautology.
>>>> This explains why you think your H is correct.
>>> It's only a tautology in systems in which excluded middle holds.
>>>
>> All expressions of formal or natural language are
>> (a) True
>> (b) False
>> (c) Not a truth bearer
> Lets try that again...
>
> (a) Truth-bearer
> 1. True
> 2. False
> (b) Not a truth bearer
> (c) As yet undetermined whether (a); or (b)

https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
If the only way to determine that the above is true is to test every
element of the set of natural numbers then it may be (c).

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