On 12/14/22 10:22 AM, olcott wrote:
> 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.
>>
>
> 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.
>

On 12/14/22 10:27 AM, olcott wrote:
> 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.
>
> My definitions are a stipulated clarification to the analytic versus
> synthetic distinction. Analytic truth is the set of expressions of
> language that can be verified as true on the basis of their meaning
> without relying on any sense data from the sense organs.
>
> I am seeing my KJV bible on my TV table right now relies on my eyesight
> and it thus not an analytic expression of language.

On 12/14/22 10:30 AM, olcott wrote:
> On 12/13/2022 8:38 PM, Richard Damon wrote:
>> On 12/13/22 10:56 AM, olcott wrote:
>>
>>> 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,
>
> It may seem that way to outside observers. Those that have experienced
> my experiences first-hand understand that my assessment is reasonably
> plausible.
>
>

Which is exactly the sort of things an insane person would say.

Youy fail.

On 12/14/22 10:36 AM, olcott wrote:
> On 12/13/2022 8:38 PM, Richard Damon wrote:
>> On 12/13/22 10:56 AM, olcott wrote:
>> 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.
>
> <sarcasm>
> Yes maybe there is a possible world where the feline animal of a cat is
> also an office building. This makes perfect sense to me. When this cat
> sits on your lap and purrs you are crushed by its thousands of tons of
> weight.
> </sarcasm>
>

Nope, you show you lack of understanding. You don't seem to understand
the difference between a universal statement and a statment of existance.

This shows your ignorance. You logic if FULL of these sorts of Fallacies.

If the context is Feline vs Canine, there are in different groups.

If the context is Animal vs Vegetable, there are NOT in different groups.

Since the model we are working in matters, it is not a Tautology.

On 12/14/22 10:39 AM, olcott wrote:
> On 12/13/2022 8:38 PM, Richard Damon wrote:
>> On 12/13/22 10:56 AM, olcott wrote:

>>>
>>> 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.
>
> That you disagree with stipulated definitions is an example of dishonesty.
>

The problem is that you try to stipluate definitions that aren't actuall
part of the field.

You keep trying to stipulate that only things that are KNOWN are True,
which isn't a correct statement.

That just proves you are not working in the right field.

On 12/14/22 9:41 AM, olcott wrote:
> 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:

Note, you siad KNOWLEDGE.
>
> (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

thus, you are talking about KNOWLEDGE, not TRUTH.

>
> 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.

No, it doesn't.

Undecided propositions are just undecided, and perhaps are NEVER
decidable, and thus unknowable. Mathematics accepts that.

You may not, but that is because you are an idiot.

>
>>> 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 12/14/22 8:19 AM, Skep Dick wrote:
> 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!

And whats the problem.

Since all the SIZEs are "Countable Infinite", there is no problem,
because of the derived rules of mathematics of infinities.

There is no problem that x + x = x, if x is an infinity.

On 12/14/22 9:18 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).

When dealing with possible infinite sets, one definition of "same size"
is that there can be a bijection made between the two sets, i.e. you can
build a one-to-one mapping between the sets such that EVERY element in
one set is mapped to PRECISELY a unique element in the other. If that
can be done, then the sets are defined to be the same size.

Note, there may be other mappings between the sets that have left overs
on one side or the other (even an infinite number of them), but if a
bijection exists, then they are the same size.

This definition also works for finite sets.

Note also, that when you get into infinities, many (if not most) of the
comfortable rules we are used to just

This IS a field that I have studied (an not just learned by rote) over
the many years of my life.

I wil also note that I have a minor learning disability that makes it
very hard to learn things "by rote", but I need to have at least good
understanding of WHY things work the way they do to remember them.

>
>> 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 12/14/22 10:59 AM, olcott wrote:
> On 12/13/2022 8:38 PM, Richard Damon wrote:
>> On 12/13/22 10:56 AM, olcott wrote:

>>> 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.
>
> I have made it my life's work to correctly understand the notion of
> truth so completely that I can correct the key errors with the currently
> received view.

The why do you still confuse Truth with Knowledge?

>
> The current received view is that the notion of analytic truth cannot be
> formalized because Tarski could not prove that the self-contradictory
> sentence of the liar paradox is true. It never occurred to Tarski that
> self-contradictory sentences are not true.

No, that is NOT what Tarski is saying (at least as I understand the
fragment, this isn't something I have studied a lot).

What he is saying is that even in the Metalanguage, we can't create a
definition that will ALWAYS tell us if a statement in the language is
True or not. Not only are somethings not provable/disprovable in the
language, but even in the metalanguage, some things in the language are
still unknown.

>
> https://liarparadox.org/Tarski_247_248.pdf
> Theorem I defines the Liar Paradox basis of the Tarski proof, it is
> referenced as Th. I below:
>
> In accordance with the first part of Th. I we can obtain the negation of
> one of the sentences in condition (α) of convention T of § 3 as a
> consequence of the definition of the symbol 'Pr' (provided we replace
> 'Tr' in this convention by 'Pr').
>
> In other words we can construct a sentence x of the science in question
> which satisfies the following condition:
> it is not true that x ∈ Pr if and only if p
>
> or in equivalent formulation:
> (1) x ∉ Pr if and only if p
> where the symbol 'p' represents the whole sentence x
> https://liarparadox.org/Tarski_275_276.pdf
>

You logic system ends up with the flaw that you can't classify a
statement as a truth bearer until you can determine that it is True or
False. Even statements that MUST be either True or False aren't Truth
Bearers in you system until you can find their truth value.

Thus, you can't actually formulate a valid statement about something you
want to find out the truth of, because that statement isn't a Truth Bearer.

On 12/14/2022 7:33 PM, Richard Damon wrote:
> On 12/14/22 10:59 AM, olcott wrote:
>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>> On 12/13/22 10:56 AM, olcott wrote:
>
>>>> 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.
>>
>> I have made it my life's work to correctly understand the notion of
>> truth so completely that I can correct the key errors with the currently
>> received view.
>
> The why do you still confuse Truth with Knowledge?
>
>>
>> The current received view is that the notion of analytic truth cannot be
>> formalized because Tarski could not prove that the self-contradictory
>> sentence of the liar paradox is true. It never occurred to Tarski that
>> self-contradictory sentences are not true.
>
> No, that is NOT what Tarski is saying (at least as I understand the
> fragment, this isn't something I have studied a lot).
>
> What he is saying is that even in the Metalanguage, we can't create a
> definition that will ALWAYS tell us if a statement in the language is
> True or not. Not only are somethings not provable/disprovable in the
> language, but even in the metalanguage, some things in the language are
> still unknown.
>
>>
>> https://liarparadox.org/Tarski_247_248.pdf
>> Theorem I defines the Liar Paradox basis of the Tarski proof, it is
>> referenced as Th. I below:
>>
>> In accordance with the first part of Th. I we can obtain the negation of
>> one of the sentences in condition (α) of convention T of § 3 as a
>> consequence of the definition of the symbol 'Pr' (provided we replace
>> 'Tr' in this convention by 'Pr').
>>
>> In other words we can construct a sentence x of the science in
>> question which satisfies the following condition:
>> it is not true that x ∈ Pr if and only if p
>>
>> or in equivalent formulation:
>> (1) x ∉ Pr if and only if p
>> where the symbol 'p' represents the whole sentence x
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> You logic system ends up with the flaw that you can't classify a
> statement as a truth bearer until you can determine that it is True or
> False. Even statements that MUST be either True or False aren't Truth
> Bearers in you system until you can find their truth value.
>
> Thus, you can't actually formulate a valid statement about something you
> want to find out the truth of, because that statement isn't a Truth Bearer.

Tarski's huge mistake was that he never bothered to notice that self
contradictory expressions of language are simply not true.

It is very important to understand Tarski because his Undefinability
theorem is a precise isomorphism of Gödel's incompleteness theorem after
all of the purely extraneous complexity has been removed.

Tarski's sentence can be proved in his metatheory only because it ceases
to be self-contradictory in his metatheory. It is exactly the same way
with Gödel.

As Andre seemed to have an impossibly difficult time understanding: as
soon as we can determine that a sentence is self-contradictory we can
determine that it is not a truth bearer.

--
Copyright 2022 Olcott

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

On 12/14/22 10:39 PM, olcott wrote:
> On 12/14/2022 7:33 PM, Richard Damon wrote:
>> On 12/14/22 10:59 AM, olcott wrote:
>>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>>> On 12/13/22 10:56 AM, olcott wrote:
>>
>>>>> 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.
>>>
>>> I have made it my life's work to correctly understand the notion of
>>> truth so completely that I can correct the key errors with the currently
>>> received view.
>>
>> The why do you still confuse Truth with Knowledge?
>>
>>>
>>> The current received view is that the notion of analytic truth cannot be
>>> formalized because Tarski could not prove that the self-contradictory
>>> sentence of the liar paradox is true. It never occurred to Tarski that
>>> self-contradictory sentences are not true.
>>
>> No, that is NOT what Tarski is saying (at least as I understand the
>> fragment, this isn't something I have studied a lot).
>>
>> What he is saying is that even in the Metalanguage, we can't create a
>> definition that will ALWAYS tell us if a statement in the language is
>> True or not. Not only are somethings not provable/disprovable in the
>> language, but even in the metalanguage, some things in the language
>> are still unknown.
>>
>>>
>>> https://liarparadox.org/Tarski_247_248.pdf
>>> Theorem I defines the Liar Paradox basis of the Tarski proof, it is
>>> referenced as Th. I below:
>>>
>>> In accordance with the first part of Th. I we can obtain the negation of
>>> one of the sentences in condition (α) of convention T of § 3 as a
>>> consequence of the definition of the symbol 'Pr' (provided we replace
>>> 'Tr' in this convention by 'Pr').
>>>
>>> In other words we can construct a sentence x of the science in
>>> question which satisfies the following condition:
>>> it is not true that x ∈ Pr if and only if p
>>>
>>> or in equivalent formulation:
>>> (1) x ∉ Pr if and only if p
>>> where the symbol 'p' represents the whole sentence x
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> You logic system ends up with the flaw that you can't classify a
>> statement as a truth bearer until you can determine that it is True or
>> False. Even statements that MUST be either True or False aren't Truth
>> Bearers in you system until you can find their truth value.
>>
>> Thus, you can't actually formulate a valid statement about something
>> you want to find out the truth of, because that statement isn't a
>> Truth Bearer.
>
> Tarski's huge mistake was that he never bothered to notice that self
> contradictory expressions of language are simply not true.

I don't see anything about that in his paper.

Your problem seems to be that because you confuse Knowledge with Truth
you think that the statements "X is Provable" or "X is Not Provable" can
be non-truth-bearers.

There is no middle between the two statements, either X is, or it is
not, provable. We may not know the answer, but it must have one.

That is DIFFERENT than the liar's paradox, as an arbirtary statement
might not be a truth-bearer, and thus a denial of the truth of a
statement also might not be.

>
> It is very important to understand Tarski because his Undefinability
> theorem is a precise isomorphism of Gödel's incompleteness theorem after
> all of the purely extraneous complexity has been removed.
>

Right, Tarski seems to be EXTENDING Godel, and is just as true as Godel is.

> Tarski's sentence can be proved in his metatheory only because it ceases
> to be self-contradictory in his metatheory. It is exactly the same way
> with Gödel.

Godel statement was never "self-contradictory". Godel statement, in the
theory is just that some statement x can not be proven in the System.
That is a perfectly fine truth-bearing statement. ALL statements must
either be Provable or Not, as false statements and non-truth-bearers are
by definition not provable, only True statements can be proven (in a
consistent system)

In the meta-theory, we see that this statement IS the statement x, and
thus if it were false, it would mean that we are asserting that some
falsse statement could be proven true, which is impossible, and thus,
the only remaining option is for it to be True, and if it is True, then
it must be correct that it is not provable in the System.

>
> As Andre seemed to have an impossibly difficult time understanding: as
> soon as we can determine that a sentence is self-contradictory we can
> determine that it is not a truth bearer.
>

Again, you confuse Truth with Knowledge. A statement is, and has always
been, and always will remain, either a Truth Bearer (and with a specific
truth value) or a non-truth-bearer. Determining that a sentence is
self-contradictiory doesn't change that status, only moves our Knowledge
about the statement.

That a given statement is provable, or that a given statement is a
Truth-Bearer, are statments that are BY DEFINITION Truth Bearers, as
there is no possible middle ground. Where is the middle between a proof
exists (even if not found yet) or no proof can exist?

Thus, things like the "Collatz Conjecture" IS a Truth Bearer (it is
eather True or it isn't). There is no option "(C)" or we don't know,
when we talk about it Truth.

Yes, if we talk about our KNOWLEDGE of the Collatz Conjecture, for now,
we need to say we don't know, and need to realize that it is possible
that it is UNKNOWABLE, because the only way to determine the answer
requires an infinite number of steps.

Knowledge requires a finite proof to demonstrate, Truth does not, as
Truth just is.

On Wednesday, December 14, 2022 at 12:51:24 PM UTC-8, olcott wrote:
> On 12/14/2022 2:38 PM, dklei...@gmail.com wrote:
> > On Wednesday, December 14, 2022 at 12:22:16 PM UTC-8, olcott wrote:
> >> On 12/14/2022 1:51 PM, dklei...@gmail.com wrote:
> >>> On Wednesday, December 14, 2022 at 7:17:47 AM UTC-8, olcott wrote:
> >>>> 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.
> >>>>
> >>> So the nodes of the knowledge ontology do not themselves carry real-life
> >>> information. Rather they are used as a meta-language for a different
> >>> tree which has yet to be described. Am I correct?
> >> No. {cat} <is-a-type-of> {animal} is in the general knowledge ontology.
> >> "Tabby" <is-a-type-of> {cat} is in the discourse ontology.
> >>
> > Or a set of triples. A lot of people seem to feel that a set of triples is
> > the correct model for knowledge.
> >
> > When you write ontology are you assuming a tree? Can I get an ontology
> > tree by restricting myself to some one middle in the triple?
> >
> <is-a-type-of> may be implied as the type of parent/child relation
> {Thing}
> |
> {vertebrate}
> |
> {feline}
> |
> {cat}
>
> It is fun going through these extra details.

Suppose we are dealing with a finite set of things. And that Knowledge is
a set of ordered triples. Call three members of a triple its object, its
attribute and its value. One possible property of an attribute might be
that is transitive. Meaning by that if one triple is xAy and another is
yAz then xAz is also a triple. Then we can chain up the A triples to a
thing w that has no A attribute. Now w is the root of a tree.

So far as I can tell the only transitive A attribute is <is-a-type-of> and
this is your ontology. Another transitive attribute would be very
interesting.

Yes, I left out some details to concentrate on the general idea.

On Thursday, 15 December 2022 at 03:20:24 UTC+2, richar...@gmail.com wrote:
> On 12/14/22 8:19 AM, Skep Dick wrote:
> > 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!
>
> And whats the problem.
>
> Since all the SIZEs are "Countable Infinite", there is no problem,
> because of the derived rules of mathematics of infinities.
>
> There is no problem that x + x = x, if x is an infinity.

The problem is (x + x = x) ↔ (x + x - x = x - x) ↔ ( x = x - x) ↔ (x = 0)

On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
> On 12/14/2022 1:49 PM, Skep Dick wrote:
> > On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
> >> On 12/14/2022 1:39 PM, Skep Dick wrote:
> >>> How do you plan to traverse an infinite set in finite time?
> >> That may place in in (b).
> >
> > You'd have to exhaust the search to place it in (b)...
> If an exhaustive search is required and not possible in finite time then
> this counts as (b).
No, it doesn't. It counts as (c).

You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.

Skep Dick <skepdick22@gmail.com> writes:

> On Thursday, 15 December 2022 at 03:20:24 UTC+2, richar...@gmail.com wrote:
>> On 12/14/22 8:19 AM, Skep Dick wrote:
>> > 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!
>>
>> And whats the problem.
>>
>> Since all the SIZEs are "Countable Infinite", there is no problem,
>> because of the derived rules of mathematics of infinities.
>>
>> There is no problem that x + x = x, if x is an infinity.
>
> The problem is (x + x = x) ↔ (x + x - x = x - x) ↔ ( x = x - x) ↔ (x = 0)

Seriously? You think every quantity must follow the rules you learned
as a child? Of course I know you don't think so, so I'm wondering what
your point it. Just chatting?

--
Ben.

On Thursday, 15 December 2022 at 14:19:44 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Thursday, 15 December 2022 at 03:20:24 UTC+2, richar...@gmail.com wrote:
> >> On 12/14/22 8:19 AM, Skep Dick wrote:
> >> > 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!
> >>
> >> And whats the problem.
> >>
> >> Since all the SIZEs are "Countable Infinite", there is no problem,
> >> because of the derived rules of mathematics of infinities.
> >>
> >> There is no problem that x + x = x, if x is an infinity.
> >
> > The problem is (x + x = x) ↔ (x + x - x = x - x) ↔ ( x = x - x) ↔ (x = 0)
> Seriously? You think every quantity must follow the rules you learned
> as a child? Of course I know you don't think so, so I'm wondering what
> your point it. Just chatting?
My point is that there is no point. Any quantity can follow whatever rules you choose at any given point in time. And a totally different rule in the very next instant.

"No course of action could be determined by a rule, because any course of action can be made out to accord with the rule." --Wittgenstein

WITTGENSTEIN: I won’t say anything which anyone can dispute. Or if anyone does dispute it, I will let that point drop and pass on to say something else.
TURING: I understand but I don’t agree that it is simply a question of giving new meanings to words.
WITTGENSTEIN: Turing doesn’t object to anything I say. He agrees with every word.
TURING: I see your point.
WITTGENSTEIN: I don’t have a point

On 12/15/22 3:03 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 03:20:24 UTC+2, richar...@gmail.com wrote:
>> On 12/14/22 8:19 AM, Skep Dick wrote:
>>> 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!
>>
>> And whats the problem.
>>
>> Since all the SIZEs are "Countable Infinite", there is no problem,
>> because of the derived rules of mathematics of infinities.
>>
>> There is no problem that x + x = x, if x is an infinity.
>
> The problem is (x + x = x) ↔ (x + x - x = x - x) ↔ ( x = x - x) ↔ (x = 0)
>

Nope, because in mathematics with infinites you don't have those properties.

That is one of the problems with infinities.

You are assuming that all the properties of the finite numbers hold,
which they don't.

On 12/15/22 7:50 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 14:19:44 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>>> On Thursday, 15 December 2022 at 03:20:24 UTC+2, richar...@gmail.com wrote:
>>>> On 12/14/22 8:19 AM, Skep Dick wrote:
>>>>> 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!
>>>>
>>>> And whats the problem.
>>>>
>>>> Since all the SIZEs are "Countable Infinite", there is no problem,
>>>> because of the derived rules of mathematics of infinities.
>>>>
>>>> There is no problem that x + x = x, if x is an infinity.
>>>
>>> The problem is (x + x = x) ↔ (x + x - x = x - x) ↔ ( x = x - x) ↔ (x = 0)
>> Seriously? You think every quantity must follow the rules you learned
>> as a child? Of course I know you don't think so, so I'm wondering what
>> your point it. Just chatting?
> My point is that there is no point. Any quantity can follow whatever rules you choose at any given point in time. And a totally different rule in the very next instant.
>
> "No course of action could be determined by a rule, because any course of action can be made out to accord with the rule." --Wittgenstein
>
> WITTGENSTEIN: I won’t say anything which anyone can dispute. Or if anyone does dispute it, I will let that point drop and pass on to say something else.
> TURING: I understand but I don’t agree that it is simply a question of giving new meanings to words.
> WITTGENSTEIN: Turing doesn’t object to anything I say. He agrees with every word.
> TURING: I see your point.
> WITTGENSTEIN: I don’t have a point
>

And with that sort of base, you can know nothing, so your system becomes
worthless.

On Thursday, 15 December 2022 at 14:59:36 UTC+2, richar...@gmail.com wrote:
> Nope, because in mathematics with infinites you don't have those properties.
>
> That is one of the problems with infinities.
>
> You are assuming that all the properties of the finite numbers hold,
> which they don't.

Where's the objective arbiter on such things?

On Thursday, 15 December 2022 at 15:00:53 UTC+2, richar...@gmail.com wrote:
> And with that sort of base, you can know nothing, so your system becomes
> worthless.

What is the objective arbiter for "worth" ?

On 12/15/2022 1:08 AM, dklei...@gmail.com wrote:
> On Wednesday, December 14, 2022 at 12:51:24 PM UTC-8, olcott wrote:
>> On 12/14/2022 2:38 PM, dklei...@gmail.com wrote:
>>> On Wednesday, December 14, 2022 at 12:22:16 PM UTC-8, olcott wrote:
>>>> On 12/14/2022 1:51 PM, dklei...@gmail.com wrote:
>>>>> On Wednesday, December 14, 2022 at 7:17:47 AM UTC-8, olcott wrote:
>>>>>> 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.
>>>>>>
>>>>> So the nodes of the knowledge ontology do not themselves carry real-life
>>>>> information. Rather they are used as a meta-language for a different
>>>>> tree which has yet to be described. Am I correct?
>>>> No. {cat} <is-a-type-of> {animal} is in the general knowledge ontology.
>>>> "Tabby" <is-a-type-of> {cat} is in the discourse ontology.
>>>>
>>> Or a set of triples. A lot of people seem to feel that a set of triples is
>>> the correct model for knowledge.
>>>
>>> When you write ontology are you assuming a tree? Can I get an ontology
>>> tree by restricting myself to some one middle in the triple?
>>>
>> <is-a-type-of> may be implied as the type of parent/child relation
>> {Thing}
>> |
>> {vertebrate}
>> |
>> {feline}
>> |
>> {cat}
>>
>> It is fun going through these extra details.
>
> Suppose we are dealing with a finite set of things. And that Knowledge is
> a set of ordered triples. Call three members of a triple its object, its
> attribute and its value. One possible property of an attribute might be
> that is transitive. Meaning by that if one triple is xAy and another is
> yAz then xAz is also a triple. Then we can chain up the A triples to a
> thing w that has no A attribute. Now w is the root of a tree.
>
> So far as I can tell the only transitive A attribute is <is-a-type-of> and
> this is your ontology. Another transitive attribute would be very
> interesting.
>
> Yes, I left out some details to concentrate on the general idea.

struct Concept
{ char GUID[32]; // The name of a unique concept
uint64_t parent;
std::vector<uint64_t> children; // semantic properties
}

<is-a-type-of> is a semantic property that is hard-coded into the
parent/child relation. Additional semantic properties must be encoded as
children.

*Meaning Postulates (1952) by RUDOLF CARNAP* (page 70)

For example, let 'W' be a primitive predicate designating the relation
Warmer. Then 'W' is transitive, irreflexive, and hence asymmetric in
virtue of its meaning.

In the previous example of the predicate 'W,' we could lay down the
following postulates (a) for transitivity and (b) for irreflexivity;
then the statement (c) of asymmetry is L-true with respect to these two
postulates:

(a) '(x)(y)(z) (W(x,y) ∧ W(y,z) → W(x,z))' // transitivity
(b) '(x) ~W(x,x)' // irreflexivity
(c) '(x)(y) (W(x,y) → ~W(y,x))' // asymmetry

https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf

struct Concept // Warmer
{ const char GUID[32] = "d5df3883-d5d7-4f5f-bf9e-eef39bdabb4a";
uint64_t parent; // physical_change_of_temperature
std::vector<uint64_t> children; // semantic properties (a)(b)(c)
}

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

On 12/15/2022 6:12 AM, Skep Dick wrote:
> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
>> On 12/14/2022 1:49 PM, Skep Dick wrote:
>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
>>>>> How do you plan to traverse an infinite set in finite time?
>>>> That may place in in (b).
>>>
>>> You'd have to exhaust the search to place it in (b)...
>> If an exhaustive search is required and not possible in finite time then
>> this counts as (b).
> No, it doesn't. It counts as (c).
>
> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.

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

If we know that an exhaustive search is required then it counts as (b).
If we don't know whether or not an exhaustive search is required then it
counts as (c).

We can make this simpler by categorizing everything into (a) or (b) and
put the left-over ones in (c). All undecidable propositions are placed
in (b). (c) only contains currently undecided propositions.

The self-contradictory sentence of the Tarski Undefinability Theorem is
placed in (b) thus invalidating the Tarski Undefinability Theorem.

Because the Gödel incompleteness theorem forms an exact isomorphism of
Tarski's undefinability theorem any refutation of Tarski is a refutation
of Gödel. The formalized Liar paradox is an exact isomorphism.

(3) x ∉ Provable if and only if x ∈ True.
~Provable(x) ↔ True(x).
x is true if and only if x is unprovable

https://liarparadox.org/Tarski_275_276.pdf

G ↔ (F ⊬ G)
G is true if and only if G is unprovable in F

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

On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
> On 12/15/2022 6:12 AM, Skep Dick wrote:
> > On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
> >> On 12/14/2022 1:49 PM, Skep Dick wrote:
> >>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
> >>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
> >>>>> How do you plan to traverse an infinite set in finite time?
> >>>> That may place in in (b).
> >>>
> >>> You'd have to exhaust the search to place it in (b)...
> >> If an exhaustive search is required and not possible in finite time then
> >> this counts as (b).
> > No, it doesn't. It counts as (c).
> >
> > You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
> (a) Truth-bearer
> 1. True
> 2. False
> (b) Not a truth bearer
> (c) As yet undetermined whether (a); or (b)
> If we know that an exhaustive search is required then it counts as (b).
> If we don't know whether or not an exhaustive search is required then it
> counts as (c).
Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.

https://turingmachinesimulator.com/shared/vgimygpuwi

Is the statement "ZFC is inconsistent" (a), (b); or (c)?

On 12/15/2022 10:23 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
>> On 12/15/2022 6:12 AM, Skep Dick wrote:
>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
>>>>>>> How do you plan to traverse an infinite set in finite time?
>>>>>> That may place in in (b).
>>>>>
>>>>> You'd have to exhaust the search to place it in (b)...
>>>> If an exhaustive search is required and not possible in finite time then
>>>> this counts as (b).
>>> No, it doesn't. It counts as (c).
>>>
>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
>> (a) Truth-bearer
>> 1. True
>> 2. False
>> (b) Not a truth bearer
>> (c) As yet undetermined whether (a); or (b)
>> If we know that an exhaustive search is required then it counts as (b).
>> If we don't know whether or not an exhaustive search is required then it
>> counts as (c).
> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
>
> https://turingmachinesimulator.com/shared/vgimygpuwi
>
> Is the statement "ZFC is inconsistent" (a), (b); or (c)?

It took me an hour to write the part that you skipped.

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

On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
> On 12/15/2022 10:23 AM, Skep Dick wrote:
> > On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
> >> On 12/15/2022 6:12 AM, Skep Dick wrote:
> >>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
> >>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
> >>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
> >>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
> >>>>>>> How do you plan to traverse an infinite set in finite time?
> >>>>>> That may place in in (b).
> >>>>>
> >>>>> You'd have to exhaust the search to place it in (b)...
> >>>> If an exhaustive search is required and not possible in finite time then
> >>>> this counts as (b).
> >>> No, it doesn't. It counts as (c).
> >>>
> >>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
> >> (a) Truth-bearer
> >> 1. True
> >> 2. False
> >> (b) Not a truth bearer
> >> (c) As yet undetermined whether (a); or (b)
> >> If we know that an exhaustive search is required then it counts as (b).
> >> If we don't know whether or not an exhaustive search is required then it
> >> counts as (c).
> > Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
> >
> > https://turingmachinesimulator.com/shared/vgimygpuwi
> >
> > Is the statement "ZFC is inconsistent" (a), (b); or (c)?
> It took me an hour to write the part that you skipped.

Shame.

Are you going to address the question or are you going to bullshit your way out again?