Correcting the definition of VALID inference

[peteolcott]

Instead of defining valid inference this way:
It is impossible for the conclusion to be false and all of the premises are true.
¬(P ∧ ¬C) or this P → C

We define it this way:
The premises necessitate the conclusion: ◻(P ⊢ C)
p q ◻(P ⊢ C)
T T T
T F F
F T F
F F F

After this correction mathematical logic and deductive inference
correspond to the commonly understood meaning of the way provability
actually works.


--
Copyright 2019 Pete Olcott All rights reserved

"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

[Jeff Barnett]

peteolcott wrote on 9/5/2019 9:17 AM:
> Instead of defining valid inference this way:
> It is impossible for the conclusion to be false and all of the premises
> are true.
> ¬(P ∧ ¬C) or this P → C
>
> We define it this way:
> The premises necessitate the conclusion: ◻(P ⊢ C)
> p    q    ◻(P ⊢ C)
> T    T    T
> T    F    F
> F    T    F
> F    F    F
>
> After this correction mathematical logic and deductive inference
> correspond to the commonly understood meaning of the way provability
> actually works.

Congratulations! You rediscovered the "AND" operator - and soiled your
panties once again!
--
Jeff Barnett

[peteolcott]

https://en.wikipedia.org/wiki/Relevance_logic

Relevance logic aims to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is not
new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a donkey, then
two and two is four" is true when translated as a material implication, yet it seems intuitively false since a true implication must tie the antecedent and consequent together by some notion of relevance. And whether or not I'm a donkey seems in no way
relevant to whether two and two is four.

[peteolcott]

On 9/5/2019 11:39 AM, Fred wrote:

> On 05/09/2019 17:17, peteolcott wrote:
>> On 9/5/2019 11:00 AM, Jeff Barnett wrote:
>>> peteolcott wrote on 9/5/2019 9:17 AM:
>>>> Instead of defining valid inference this way:
>>>> It is impossible for the conclusion to be false and all of the premises are true.
>>>> ¬(P ∧ ¬C) or this P → C
>>>>
>>>> We define it this way:
>>>> The premises necessitate the conclusion: ◻(P ⊢ C)
>>>> p    q    ◻(P ⊢ C)
>>>> T    T    T
>>>> T    F    F
>>>> F    T    F
>>>> F    F    F
>>>>
>>>> After this correction mathematical logic and deductive inference
>>>> correspond to the commonly understood meaning of the way provability
>>>> actually works.
>>>
>>> Congratulations! You rediscovered the "AND" operator - and soiled your panties once again!
>>
>> https://en.wikipedia.org/wiki/Relevance_logic
>>
>> Relevance logic aims to capture aspects of implication that are ignored

> [...]
>
> Another change of subject.  Which among the many relevance logics writes ◻(P ⊢ C) for P & C, and what benefit arises?
>
> Pete-ee-babe, I don't want to sound rude, but your problem isn't just that you have no understanding of logic, it's that you're utterly thick.
>
>

Yet again with your deceitfulness.

You removed this key part of the referenced quote:

"if I'm a donkey, then two and two is four" is true when translated as a
material implication, yet it seems intuitively false

It is obvious to even a pea brain that something is wrong with the
way the mathematical logic is defined when it diverges from common
understanding of the way that correct reasoning actually works.

IF THE PURPOSE OF MATHEMATICAL LOGIC IS NOT TO MATHEMATICALLY FORMALIZE
THE WAY THAT CORRECT REASONING ACTUALLY WORKS THEN WHAT IS ITS PURPOSE?

[peteolcott]

That seems to be the best that I can do for propositional logic.
It does screen out the principle of explosion and "paradoxes" of material implication.

When we get into predicate logic we begin to have a basis for ensuring a semantic
relevance connection between the premises and the conclusion.

Semantic connection
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
S ∈ men ⊆ mortals
∴ S ∈ mortals

No Semantic connection
All men are mortal.
Socrates is a goat.
Therefore, Socrates is ???

[peteolcott]

On 9/5/2019 3:02 PM, Fred wrote:
> On 05/09/2019 20:57, peteolcott wrote:
>> On 9/5/2019 2:34 PM, Fred wrote:

>>> On 05/09/2019 20:14, peteolcott wrote:
>>>> On 9/5/2019 11:17 AM, peteolcott wrote:
>>>>> On 9/5/2019 11:00 AM, Jeff Barnett wrote:
>>>>>> peteolcott wrote on 9/5/2019 9:17 AM:
>>>>>>> Instead of defining valid inference this way:
>>>>>>> It is impossible for the conclusion to be false and all of the premises are true.
>>>>>>> ¬(P ∧ ¬C) or this P → C
>>>>>>>
>>>>>>> We define it this way:
>>>>>>> The premises necessitate the conclusion: ◻(P ⊢ C)
>>>>>>> p    q    ◻(P ⊢ C)
>>>>>>> T    T    T
>>>>>>> T    F    F
>>>>>>> F    T    F
>>>>>>> F    F    F
>>>>>>>
>>>>>>> After this correction mathematical logic and deductive inference
>>>>>>> correspond to the commonly understood meaning of the way provability
>>>>>>> actually works.
>>>>>>
>>>>>> Congratulations! You rediscovered the "AND" operator - and soiled your panties once again!
>>>>>
>>>>> https://en.wikipedia.org/wiki/Relevance_logic
>>>>>
>>>>> Relevance logic aims to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is
>>>>> not new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a
>>>>> donkey, then two and two is four" is true when translated as a material implication, yet it seems intuitively false since a true implication must tie the antecedent and consequent together by some notion of relevance. And whether or not I'm a donkey
>>>>> seems in no way relevant to whether two and two is four.
>>>>>
>>>>
>>>>
>>>> That seems to be the best that I can do for propositional logic.
>>>

>>> What's that?   Writing ◻(P ⊢ C) for P & C?  I'll say one thing in your favour - you're a constant source of amusement.

>>>
>>>> It does screen out the principle of explosion and "paradoxes" of material implication.
>>>

>>> Why?  How do you define material implication?
>>>
>>
>> THAT WAS IN THE PART THAT YOU IGNORED TWICE NOW
>
> How many times have you ignored the point that your ◻(P ⊢ C) is P & C?
>
>> YOU ARE OBVIOUSLY NOT INTERESTED IN AN HONEST DIALOGUE.
>
> Have you read André's claim that, according to you
>
>     violets are blue necessarily proves that phobos orbits mars.
>

We have that same problem here
p q p → q

T T T
T F F

F T T
F F T

This is even worse because it proves that {phobos orbits mars}
whether or not {violets are blue}.




> and
>
>     phobos orbits mars necessarily proves that violets are blue.
>
> which stems directly from you defining ◻(P ⊢ C) to be P & C?

[Jeff Barnett]

Have you changed your pants yet!

Do you realize that with your latest and most stupid definition, you
can't prove anything new. Not a thing. Have you thought of going to work
at Walmart in a low paid hourly job? It would use up those idle hours
where you make a buffoon of yourself. So your logic consists completely
and totally of database lookup. You can't even do: A lays in B, B lays
in C, so A lays in C without already knowing A lays in C!!!!!!!! Great
insight to all the problems of logic. I think you are addressing your
soiled panties by sticking your head up your ass. It might work in re
your wardrobe but not your logic.
--
Jeff Barnett

[António Marques]

It's been that way for a few months at least.

[peteolcott]

On 9/5/2019 11:05 AM, Fred wrote:

> On 05/09/2019 16:17, peteolcott wrote:
>> Instead of defining valid inference this way:
>> It is impossible for the conclusion to be false and all of the premises are true.
>> ¬(P ∧ ¬C) or this P → C
>>
>> We define it this way:
>> The premises necessitate the conclusion: ◻(P ⊢ C)

CORRECTED TABLE

>> P    C    ◻(P ⊢ C)

>> T    T    T
>> T    F    F
>> F    T    F
>> F    F    F
>

> I'm guessing that p and q should be P and C, or vice versa.
>
> I know you don't read what others write, but you should at least read what you write.  According to the above  ◻(P ⊢ C) is just an elaborate way of writing P & C.
>
> Also, premises come in *sets*.

I am eliminating the extraneous complexity the same way Mendelson does: Γ ⊢ C
Also we can have one premise and one conclusion
(A) Sam is fat
(B) Therefore Sam weighs a lot.
A ⊢ B

>>
>> After this correction mathematical logic and deductive inference
>> correspond to the commonly understood meaning of the way provability
>> actually works.
>

> Your notation  ◻(P ⊢ C) is quite empty unless you give a coherent account of a calculus that deals with it.
>
> Also (does this really need to be said?) if you redefine "valid inference" and anything you say about valid inference will have no bearing on what others are saying about valid inference.
>

Yes and judges will continue to take contradictory testimony as proof
that the one testifying is certainly telling the truth because they
will plug the contradiction into the principle of explosion just like
every other judge.

[André G. Isaak]

On 2019-09-05 8:59 p.m., peteolcott wrote:
> On 9/5/2019 11:05 AM, Fred wrote:
>> On 05/09/2019 16:17, peteolcott wrote:
>>> Instead of defining valid inference this way:
>>> It is impossible for the conclusion to be false and all of the
>>> premises are true.
>>> ¬(P ∧ ¬C) or this P → C
>>>
>>> We define it this way:
>>> The premises necessitate the conclusion: ◻(P ⊢ C)
>
> CORRECTED TABLE
>
>>> P    C    ◻(P ⊢ C)
>>> T    T    T
>>> T    F    F
>>> F    T    F
>>> F    F    F
>>
>> I'm guessing that p and q should be P and C, or vice versa.
>>
>> I know you don't read what others write, but you should at least read
>> what you write.  According to the above  ◻(P ⊢ C) is just an elaborate
>> way of writing P & C.
>>
>> Also, premises come in *sets*.
>
> I am eliminating the extraneous complexity the same way Mendelson does:
> Γ ⊢ C

Γ *is* a set.

> Also we can have one premise and one conclusion

Yes, that's how sets work. They can have zero or more elements.

André

> (A) Sam is fat
> (B) Therefore Sam weighs a lot.
> A ⊢ B
>
>>>
>>> After this correction mathematical logic and deductive inference
>>> correspond to the commonly understood meaning of the way provability
>>> actually works.
>>
>> Your notation  ◻(P ⊢ C) is quite empty unless you give a coherent
>> account of a calculus that deals with it.
>>
>> Also (does this really need to be said?) if you redefine "valid
>> inference" and anything you say about valid inference will have no
>> bearing on what others are saying about valid inference.
>>
>
> Yes and judges will continue to take contradictory testimony as proof
> that the one testifying is certainly telling the truth because they
> will plug the contradiction into the principle of explosion just like
> every other judge.
>


--

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

[peteolcott]

- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-
- Yes and judges will continue to take contradictory testimony as proof
- that the one testifying is certainly telling the truth because they
- will plug the contradiction into the principle of explosion just like
- every other judge.
-

[André G. Isaak]

<useless waste of bandwidth snipped>

You still really don't get the most basic fact about proofs, do you?

A ⊢ B

Does not assert the truth of A, nor does it assert the truth of B.

It asserts that B cannot be false when A is true.

(A ∧ ¬A) ⊢ B

Cannot be used to demonstrate the truth of B unless you can show the
truth of (A ∧ ¬A).

Not that courtroom antics are relevant to logic, but if one attempted to
demonstrate in court the truth of B using (A ∧ ¬A) ⊢ B, they would first
need to demonstrate the truth of (A ∧ ¬A).

André

[peteolcott]

Yet that is not how proofs actually work in reality.

> (A ∧ ¬A) ⊢ B
>

This says that a contradiction necessitates a truth.
This says that a contradiction necessitates a truth.
This says that a contradiction necessitates a truth.
This says that a contradiction necessitates a truth.
This says that a contradiction necessitates a truth.

That is NOT the way that truth actually works.

There is never any case where any contradiction ever actually necessitates any truth.
Contradiction ALWAYS necessitates falsity it never necessitates truth.

A contradiction in testimony is the basis for a conviction for perjury.
All that is needed is a contraction.

> Cannot be used to demonstrate the truth of B unless you can show the truth of (A ∧ ¬A).
>
> Not that courtroom antics are relevant to logic, but if one attempted to demonstrate in court the truth of B using (A ∧ ¬A) ⊢ B, they would first need to demonstrate the truth of (A ∧ ¬A).
>
> André
>


--

[André G. Isaak]

According to whom? As far as I know, that is how most people interpret
proofs. You don't. But you're only one person who has already
demonstrated some rather nonstandard views on a whole range of topics.

>
>> (A ∧ ¬A) ⊢ B
>>
>
> This says that a contradiction necessitates a truth.
> This says that a contradiction necessitates a truth.
> This says that a contradiction necessitates a truth.
> This says that a contradiction necessitates a truth.
> This says that a contradiction necessitates a truth.
> That is NOT the way that truth actually works.
>
> There is never any case where any contradiction ever actually
> necessitates any truth.

> Contradiction ALWAYS necessitates falsity it never necessitates truth.

So are you now claiming that (A ∧ ¬A) can be used to prove that any
arbitrary proposition is false?

i.e. (A ∧ ¬A) proves that it is false that I breathe air?

And exactly how are you defining 'necessitates'? In your previous posts
you started using ◻. Do you actually know how this operator is formally
defined? Can you explain the difference between:

A,
◇A, and
◻A ?

What about the difference between:

◻◇A,
◇◻A, and
◻◻A ?

If you can't, then you should stop using the symbol.

> A contradiction in testimony is the basis for a conviction for perjury.
> All that is needed is a contraction.

Courtroom proceedings don't make use of formal logic. And a
contradiction in testimony is not sufficient for a conviction for
perjury. Otherwise there would be a hell of a lot more people in jail
for perjury.

André

>> Cannot be used to demonstrate the truth of B unless you can show the
>> truth of (A ∧ ¬A).
>>
>> Not that courtroom antics are relevant to logic, but if one attempted
>> to demonstrate in court the truth of B using (A ∧ ¬A) ⊢ B, they would
>> first need to demonstrate the truth of (A ∧ ¬A).
>>
>> André
>>
>
>


--

[peteolcott]

I am claiming that Reductio ad absurdum proves that the proposition is false.

Top of page 320:
http://liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf

The contradiction tells us that our assumption of the existence
of H, and hence the assumption of the decidability of the halting
problem, must be false.

> i.e. (A ∧ ¬A) proves that it is false that I breathe air?
>
> And exactly how are you defining 'necessitates'? In your previous posts you started using ◻. Do you actually know how this operator is formally defined? Can you explain the difference between:
>
> A,
> ◇A, and
> ◻A ?
>
> What about the difference between:
>
> ◻◇A,
> ◇◻A, and
> ◻◻A ?
>
> If you can't, then you should stop using the symbol.
>
>> A contradiction in testimony is the basis for a conviction for perjury.
>> All that is needed is a contraction.
>
> Courtroom proceedings don't make use of formal logic. And a contradiction in testimony is not sufficient for a conviction for perjury. Otherwise there would be a hell of a lot more people in jail for perjury.
>
> André
>
>>> Cannot be used to demonstrate the truth of B unless you can show the truth of (A ∧ ¬A).
>>>
>>> Not that courtroom antics are relevant to logic, but if one attempted to demonstrate in court the truth of B using (A ∧ ¬A) ⊢ B, they would first need to demonstrate the truth of (A ∧ ¬A).
>>>
>>> André
>>>
>>
>>
>
>


--

[André G. Isaak]

Reductio ad absurdum is what provides the proof that the POE holds true.
(or at least it is one of many things which can provide this proof).

[peteolcott]

Top of page 320:
http://liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
The contradiction tells us that our assumption of the existence
of H, and hence the assumption of the decidability of the halting
problem, must be false.

I am claiming that Reductio ad absurdum proves that the proposition is false.

Top of page 320:
http://liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
The contradiction tells us that our assumption of the existence
of H, and hence the assumption of the decidability of the halting
problem, must be false.

I am claiming that Reductio ad absurdum proves that the proposition is false.

Top of page 320:
http://liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
The contradiction tells us that our assumption of the existence
of H, and hence the assumption of the decidability of the halting
problem, must be false.

I am claiming that Reductio ad absurdum proves that the proposition is false.

Top of page 320:
http://liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
The contradiction tells us that our assumption of the existence
of H, and hence the assumption of the decidability of the halting
problem, must be false.

[André G. Isaak]

Your repetition accomplishes utterly nothing.

Do you actually understand what 'reductio ad absurdum' means (as a term
of art, not its Latin meaning) or is this just another phrase you've
picked up and decided to use? Can you paraphrase it?

[Ben Bacarisse]

André G. Isaak <agi...@gm.invalid> writes:
> On 2019-09-05 11:44 p.m., peteolcott wrote:

<stuff repeated dozens of times>

> Your repetition accomplishes utterly nothing.

Oh, I disagree. I think the childish repetition and ALL CAPS tantrums
are very helpful to casual readers. It helps them not who to pay more
or less attention to.

--
Ben.

[peteolcott]

Do you understand that "Reductio ad absurdum" + "The principle of explosion"
creates an inconsistent system?

RAA derives a contradiction proving that a proposition is false.
(as shown by the concrete example above).

This same contradiction becomes the premises of POE which proves
the same proposition true.

[peteolcott]

IT WOULD BE HELPFUL IF YOU DID NOT REMOVE THE IMMEDIATE CONTEXT.
MOST PEOPLE HERE REMOVE THE IMMEDIATE CONTEXT SO THAT THE OBVIOUS
ERROR OF THEIR CRITIQUE IS NOT DIRECTLY SEEN AS A FLAT OUT LIE.

On 9/6/2019 12:26 AM, peteolcott wrote:
> I am claiming that Reductio ad absurdum proves that the proposition is false.
>
> Top of page 320:
> http://liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
>
> The contradiction tells us that our assumption of the existence
> of H, and hence the assumption of the decidability of the halting
> problem, must be false.

On 9/6/2019 4:57 AM, Transfinite Numbers wrote:
> Yes, you got this valid inference rule:
>
> G, A |- f
> -----------
> G |- ~A
>
> But it doesn't say that A is false (~A). It only says
> that A is false (~A) relative to the background knowledge
> G you were feeding to the logic.
>

I can't tell what you are saying there. It looks like you are concluding:
G ⊢ ¬A on the basis of {G, A} ⊢ f


> Well it is called "propositional" logic. So a propositional
> variable kind of proposes a truth value. It is not that
> when I write:
>
> pigs can fly
>
> That the above sentence is false. Because as a logical
> sentence it only proposes the truth of that every
> individual that is a pig, can also fly.
>
> Logic only uses what is written, and has no world
> knowledge. So you cannot deduce:
>
> pigs can fly => false
>
> On the other hand if you feed the logic world knowledge,
> you get more and more refined deductions. Like
> if you add the following facts:
>
> <BACKGROUND_KNOWLEDGE>
> pigs cannot fly
>
> Then you will already see that:
>
> <BACKGROUND_KNOWLEDGE> |- pigs can fly => false
>
> Maybe you guys should crawl from under your rocks.
> Such stuff was done in the 80's even on the computer.
> Just check for example KL-ONE, A-Box, T-Box etc..
>
> KL‐ONE Knowledge Representation System
> http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.545.601
>
> Every student nowadays that takes an AI course, should
> have a grip what role logic plays in modelling world
> knowledge. Logic itself doesn't know anything
>
> about the world.
>
That was all very well done.
Now let's get back to the point.

Since a contradiction proves that a sentence is false
a contradiction cannot be used as the basis to prove
that anything is true.

[peteolcott]

I will no longer tolerate it when my most important points
are ignored.

[André G. Isaak]

I'd asked if you could paraphrase reductio ad absurdum. The fact that
you chose not to to me indicates that you do not understand it.

> Do you understand that "Reductio ad absurdum" + "The principle of
> explosion"
> creates an inconsistent system?
>
> RAA derives a contradiction proving that a proposition is false.
> (as shown by the concrete example above).

Which example above?

> This same contradiction becomes the premises of POE which proves
> the same proposition true.

in RAA, in order to prove Γ ⊢ C, one takes a set consisting of the
premises contained in Γ along with ¬C and demonstrates that this set
contains a contradiction. If it does, the original conclusion C is shown
to be true.

If Γ contains a contradiction, then a set formed by the elements of Γ
and ¬C will _always_ contain a contradiction, hence the principle of
explosion.

This does *not* create an inconsistent system. If you maintain that it
does, please illustrate the inconsistency which it creates using a
concrete example (your description above is one which I cannot follow).

[Ben Bacarisse]

peteolcott <Here@Home> writes:

> On 9/6/2019 6:42 AM, Ben Bacarisse wrote:
>> André G. Isaak <agi...@gm.invalid> writes:
>>> On 2019-09-05 11:44 p.m., peteolcott wrote:
>> <stuff repeated dozens of times>
>>
>>> Your repetition accomplishes utterly nothing.
>>
>> Oh, I disagree. I think the childish repetition and ALL CAPS tantrums
>> are very helpful to casual readers. It helps them not who to pay
>> more

s/not/know/

>> or less attention to.
>
> I will no longer tolerate it when my most important points
> are ignored.

What will you do? Thcream, an' thcream an' thcream till your thick?
(Showing my age there...)

--
Ben.

[peteolcott]

Whenever I ridiculously repeat the point that has been ignored
the point is then addressed.

[peteolcott]

On 9/6/2019 12:26 PM, George Greene wrote:

> On Thursday, September 5, 2019 at 11:17:49 AM UTC-4, peteolcott wrote:
>> Instead of defining valid inference this way:
>> It is impossible for the conclusion to be false and all of the premises are true.
>> ¬(P ∧ ¬C) or this P → C
>>
>> We define it this way:
>> The premises necessitate the conclusion: ◻(P ⊢ C)
>

> That's NOT different.
>
> That's what "necessitate" MEANS.
> It's a shame that you didn't know that your
> ⊢
> ALREADY MEANS
> ◻ ( -> ).
> The derivability thing is just the necessity of the implication.
>

In ordinary correct reasoning everyone fully knows that a contradiction
ONLY proves falsehood. I am trying to formalize this so that mathematical
logic always behaves this same way.

[Keith Thompson]

peteolcott <Here@Home> writes:
[...]

> Whenever I ridiculously repeat the point that has been ignored
> the point is then addressed.

Then let me make a suggestion to everyone else participating in this
discussion. If Pete writes something repeatedly, simply ignore it.
Consider what behavior you're encouraging, and whether you really want
to encourage it.

--
Keith Thompson (The_Other_Keith) ks...@mib.org <http://www.ghoti.net/~kst>
Will write code for food.
void Void(void) { Void(); } /* The recursive call of the void */

[peteolcott]

On 9/6/2019 5:02 PM, Fred wrote:
> On 06/09/2019 23:00, peteolcott wrote:
>
>>>
>>> Have you given up on relevance logics?  Thrown on the scrap heap with MTT, C++, Prolog, ... are they?
>>>
>>>
>> NO I HAVE NOT GIVEN UP ION ANYTHING. I JUST FRIGGING SAID THAT.
>
> Which one have you chosen?
>

I keep switching back and forth until someone understands what I am saying.
My point is concurrently made by all of those different ways. So far
no one has understood any of them, except that David Kleinecke agreed with me about POE.

On 8/27/2019 11:25 PM, David Kleinecke wrote:> On Tuesday, August 27, 2019 at 8:39:49 PM UTC-7, peteolcott wrote:
> The point being that once the thinker reaches the contradiction
> they stop following that line of thought.
>
> The question is - suppose we ignore the contradiction signal
> and rather try to continue reasoning past having both P and ~P.
> We will be confronted by
> P /\ ~P -> Q
> This cause the entire reasoning machine to declare "tilt" and
> meaningful reasoning of all kinds must stop.
>
> The difference discussed in the thread are only about how that
> tilt is expressed. The standard approach been to declare all
> propositions true - the Principle of Explosion. Other signals
> are possible.
>
> What matters is that we must not reason past the contradiction.
>

Reasoning past a contradiction is like continuing the arithmetic
after a Divide-By-Zero UNDEFINED error.

[peteolcott]

On 9/6/2019 4:28 PM, Keith Thompson wrote:
> peteolcott <Here@Home> writes:
> [...]
>> Whenever I ridiculously repeat the point that has been ignored
>> the point is then addressed.
>
> Then let me make a suggestion to everyone else participating in this
> discussion. If Pete writes something repeatedly, simply ignore it.
> Consider what behavior you're encouraging, and whether you really want
> to encourage it.
>

I will not tolerate being treated unreasonably.

[David Kleinecke]

I was describing how mathematical proofs actually work.
With a possible few exceptions they do not use formal logic.

Consider the largest prime.
Assume there is a largest prime
There are only a finite number of primes
Multiply all the primes together and add one
Prove (as a lemma) this new number is not divisible by any prime
Prove (an existing theorem) there is a prime that divides the new number
By last two there is a contradiction and the assumption must be false
Conclude there is no largest prime.

None of this has much resemblance to formal logic

[peteolcott]

On 9/6/2019 5:12 PM, Fred wrote:

> On 05/09/2019 16:17, peteolcott wrote:
>> Instead of defining valid inference this way:
>> It is impossible for the conclusion to be false and all of the premises are true.
>> ¬(P ∧ ¬C) or this P → C
>>
>> We define it this way:
>> The premises necessitate the conclusion: ◻(P ⊢ C)

>> P    C    ◻(P ⊢ C)
>> T    T    T
>> T    F    F
>> F    T    F
>> F    F    F
>

> Supposing that either p and q are P and C or vice versa, why are you using two symbols, that already have a use, to mean &?

If P is a set of premises and C is the deductive conclusion we know
that C is true if P is true otherwise we lack a sufficient basis for
knowing that P is true.

THIS IS THE WAY THAT GENERIC CONCEPT OF PROOF ACTUALLY WORKS.

>
>> After this correction mathematical logic and deductive inference
>> correspond to the commonly understood meaning of the way provability
>> actually works.
>>
>>
>

[peteolcott]

On 9/6/2019 6:40 PM, Eram semper recta wrote:

> On Friday, 6 September 2019 19:18:17 UTC-4, peteolcott wrote:
>> On 9/6/2019 5:12 PM, Fred wrote:
>>> On 05/09/2019 16:17, peteolcott wrote:
>>>> Instead of defining valid inference this way:
>>>> It is impossible for the conclusion to be false and all of the premises are true.
>>>> ¬(P ∧ ¬C) or this P → C
>>>>
>>>> We define it this way:
>>>> The premises necessitate the conclusion: ◻(P ⊢ C)
>>>> P    C    ◻(P ⊢ C)
>>>> T    T    T
>>>> T    F    F
>>>> F    T    F
>>>> F    F    F
>>>
>>> Supposing that either p and q are P and C or vice versa, why are you using two symbols, that already have a use, to mean &?
>>
>> If P is a set of premises and C is the deductive conclusion we know
>> that C is true if P is true otherwise we lack a sufficient basis for
>> knowing that P is true.
>>
>> THIS IS THE WAY THAT GENERIC CONCEPT OF PROOF ACTUALLY WORKS.
>

> You mean it's actually that simple?! No obfuscation?! No conflation?! Chuckle. Good luck Pete. Just remember you are dealing with a Simian crowd whose egos are far bigger than their pitifully low IQs.

Thanks very much for the moral support !!!

[peteolcott]

None-the-less you affirmed my key point:

>> > What matters is that we must not reason past the contradiction.

When the principle of explosion [reasons past the contradiction] it makes
mathematical logic inconsistent because the same contradiction that proves
proposition P is false using Reductio ad absurdum also proves this same
proposition P is true.

> Consider the largest prime.
> Assume there is a largest prime
> There are only a finite number of primes
> Multiply all the primes together and add one
> Prove (as a lemma) this new number is not divisible by any prime
> Prove (an existing theorem) there is a prime that divides the new number
> By last two there is a contradiction and the assumption must be false
> Conclude there is no largest prime.
>
> None of this has much resemblance to formal logic
>
>

[peteolcott]

On 9/7/2019 12:27 PM, Fred wrote:

> On 07/09/2019 18:11, peteolcott wrote:
>
>> When the principle of explosion [reasons past the contradiction] it makes
>> mathematical logic inconsistent because the same contradiction that proves
>

> The same contradiction that *proves*...  I.e., you're starting with a contradiction *not* deducing one.  Deduce A&~A from (whatever you mean by) mathematical logic.  You can't.  You don't even know that that's what you need to do to show something
> inconsistent.
>

We simply form an inference chain of Reductio ad absurdum with the principle of explosion.
Rules-of-inference can be chained right?

Proposition Y derives contradiction X proving that Y is false.
Proposition Y derives contradiction X applied to the Principle of Explosion proving that Y is true.
Therefore Y is false and Y is true unless we reject POE as a valid rule-of-inference.

>> proposition P is false using Reductio ad absurdum also proves this same
>> proposition P is true.
>
>
>>
>>
>>> Consider the largest prime.
>>>     Assume there is a largest prime
>>>     There are only a finite number of primes
>>>     Multiply all the primes together and add one
>>>     Prove (as a lemma) this new number is not divisible by any prime
>>>     Prove (an existing theorem) there is a prime that divides the new number
>>>     By last two there is a contradiction and the assumption must be false
>>>     Conclude there is no largest prime.
>>>
>>> None of this has much resemblance to formal logic
>

> Who wrote "None of this has much resemblance to formal logic", Pete Olcott or David Kleinecke?

[David Kleinecke]

On Saturday, September 7, 2019 at 11:49:53 AM UTC-7, peteolcott wrote:
> On 9/7/2019 12:27 PM, Fred wrote:
> >
> > Who wrote "None of this has much resemblance to formal logic", Pete Olcott or David Kleinecke?

I did it - with my little hatchet.

[peteolcott]

On 9/7/2019 2:55 PM, David Petry wrote:
>
>
> peteolcott wrote:
>
>> It is obvious to even a pea brain that something is wrong with the
>> way the mathematical logic is defined when it diverges from common
>> understanding of the way that correct reasoning actually works.
>
>> IF THE PURPOSE OF MATHEMATICAL LOGIC IS NOT TO MATHEMATICALLY FORMALIZE
>> THE WAY THAT CORRECT REASONING ACTUALLY WORKS THEN WHAT IS ITS PURPOSE?
>
>
> You make a good point, but I'm not sure that you have corrected the problems with mathematical logic.
>
> One thing I suggest that you consider is a three valued logic.
(a) True
(b) False
(c) Incorrect

> That is, as in science, a valid statement must make a prediction. In science, of course, those will be predictions about real world phenomena. In mathematics, they will be predictions about computational phenomena. Then if a statement makes a correct prediction, the statement is said to be true. If it make a false prediction, the statement is false. And if it makes no prediction at all, then the statement is vacuous. (true, false, vacuous) And note that in Cantorian set theory, there is a lot going on that is vacuous.
>
> Furthermore, consider that mathematics has a natural semantics. The semantics (or meaning) of a statement may be equated with the collection of all predictions that the statement makes. Then reasoning about statements must be equivalent to reasoning about the semantics. That should make mathematical reasoning closer to what you are calling "correct reasoning".
>
> One more thing you might try, is to try to formalize the reasoning involved in what is called the Socratic Method. Again, that would help make it clear what "correct reasoning" is.

Conceptual truth is a set of mutually self-defining interlocking semantic tautologies.

Conceptual truth is a set of relations between finite strings defined to have the semantic property of Boolean True.

[temako...@gmail.com]

more garbage from the psycho-shitter Péter la Crotte, on sci.lang.

[peteolcott]

> FWIW, that really doesn't clarify things for me.
>

You know how the operation of arithmetic works on strings of numeric digits right?
"2 + 3 = 5" is true and provable on the basis of the algorithm that defines the
relations in that string. "2 + 3" is defined to have an "=" relation to "5".
In philosophy of math it is said that "2 + 3" satisfies the "=" relation to "5".
All conceptual truth works this same way.

"cats" are defined to have the "type of" relation to "animals".
The entire set of conceptual truth can for formalized as these same
relations between finite strings.

There is never a case where a conceptual truth cannot be formalized
as a relation between finite strings, thus refuting Tarski Undefinability.
There is never a case where the satisfaction of these relations does
not concurrently specify provability and truth, thus refuting 1931
Incompleteness.

[peteolcott]

On 9/8/2019 9:33 AM, Fred wrote:
> On 07/09/2019 20:10, Fred wrote:

>> On 07/09/2019 19:49, peteolcott wrote:
>>> On 9/7/2019 12:27 PM, Fred wrote:
>>>> On 07/09/2019 18:11, peteolcott wrote:
>>>>
>>>>> When the principle of explosion [reasons past the contradiction] it makes
>>>>> mathematical logic inconsistent because the same contradiction that proves
>>>>
>>>> The same contradiction that *proves*...  I.e., you're starting with a contradiction *not* deducing one.  Deduce A&~A from (whatever you mean by) mathematical logic.  You can't.  You don't even know that that's what you need to do to show something
>>>> inconsistent.
>>>>
>>>
>>> We simply form an inference chain of Reductio ad absurdum with the
>>

>> If it's simple, do it!  Start with Mendelson's propositional calculus and prove A and ~A as theorems, for some formula A.

>>
>>> principle of explosion.
>>> Rules-of-inference can be chained right?
>>>
>>> Proposition Y derives contradiction X proving that Y is false.
>>> Proposition Y derives contradiction X applied to the Principle of Explosion proving that Y is true.
>>> Therefore Y is false and Y is true unless we reject POE as a valid rule-of-inference.
>>

>> POE and RAA are derived rules of Mendelson's PC.
>
> The soundness of PC is the easiest metaproof in the whole of logic.
> The axioms are all tautologies.  The rule of inference transmits tautologousness.  Therefore the theorems are all tautologies.
>

All of mathematical logic works this same way. ONLY incorrect reasoning
shows otherwise. There are a set of finite strings comprising the axioms,
rules-of-inference and axiom schemata** of each formal system / body of
conceptual knowledge.

The satisfaction of sequences of these finite strings concurrently defines
true and provable whenever the set of premises Γ is empty:

*Introduction to Mathematical logic Sixth edition Elliott Mendelson (2015):28*
sequence B1, …, Bk of wfs such that C is Bk and, for each i,
either Bi is an axiom or Bi is in Γ, or Bi is a direct consequence
by some rule of inference of some of the preceding wfs in the sequence.

** axiom schemata algorithmically compress an infinite set of axioms
making the list of axioms, rules-of-inference and axiom schemata
a finite list.

For example the set of all relations between finite strings of numeric
digits for this relational operator: "=" and this function: "+" is
specified by its corresponding algorithm.

[peteolcott]

On 9/9/2019 10:57 AM, Fred wrote:

> On 09/09/2019 15:38, peteolcott wrote:
>> On 9/8/2019 9:33 AM, Fred wrote:
>>> On 07/09/2019 20:10, Fred wrote:
>>>> On 07/09/2019 19:49, peteolcott wrote:
>>>>> On 9/7/2019 12:27 PM, Fred wrote:
>>>>>> On 07/09/2019 18:11, peteolcott wrote:
>>>>>>
>>>>>>> When the principle of explosion [reasons past the contradiction] it makes
>>>>>>> mathematical logic inconsistent because the same contradiction that proves
>>>>>>
>>>>>> The same contradiction that *proves*...  I.e., you're starting with a contradiction *not* deducing one.  Deduce A&~A from (whatever you mean by) mathematical logic.  You can't.  You don't even know that that's what you need to do to show something
>>>>>> inconsistent.
>>>>>>
>>>>>
>>>>> We simply form an inference chain of Reductio ad absurdum with the
>>>>
>>>> If it's simple, do it!  Start with Mendelson's propositional calculus and prove A and ~A as theorems, for some formula A.
>>>>
>>>>> principle of explosion.
>>>>> Rules-of-inference can be chained right?
>>>>>
>>>>> Proposition Y derives contradiction X proving that Y is false.
>>>>> Proposition Y derives contradiction X applied to the Principle of Explosion proving that Y is true.
>>>>> Therefore Y is false and Y is true unless we reject POE as a valid rule-of-inference.
>>>>
>>>> POE and RAA are derived rules of Mendelson's PC.
>>>
>>> The soundness of PC is the easiest metaproof in the whole of logic.
>>> The axioms are all tautologies.  The rule of inference transmits tautologousness.  Therefore the theorems are all tautologies.
>>>
>>
>> All of mathematical logic works this same way. ONLY incorrect reasoning
>

> Try not to change the subject.  The idea that you know anything about *all* of mathematical logic is preposterous.

That I know the fundamental architecture upon which all mathematics is derived is not preposterous at all.
Every formalist knows that its all a matter of relations between finite strings.

I clarified this formalist perspective and provided the next level of specificity by elaborating some detail
about the nature of these relations.

This perspective cannot possibly be derived through the learned-by-rote frame-of-reference.

If you are not merely a dishonest Troll, then you are an honest logician that is woefully
deficient in the philosophy aspect of the philosophy of mathematics.

> I took 14 graduate courses on the subject and three undergraduate courses, and that just scratched the surface.  But anyway back to the
> subject in hand...
>
> Consider Mendelson's propositional calculus which I'll call PC.  POE and RAA are derived rules of Mendelson's PC.  So, according to you, PC is inconsistent.  That means you need to prove one of two things, either
> a) for some formula A (your choice) both |-A and |-~A; or
> b) for some formula A (your choice) |-A & ~A  (Mendelson defines &).
> But all of PC's axioms are tautologies and its rule of inference transmits tautologousness, so if |-X the X is a tautology.  If you take path a) then your A must be such that both it and ~A are tautologies; and if you take path b) A & ~A must be a tautology.
>
> A reply to this post that does not change the subject (as if!) will consist of you doing either a) or b) or -
> c) admitting you are wrong about POE amd RAA entailing inconsistency.

[peteolcott]

On 9/10/2019 6:51 AM, Eram semper recta wrote:

> On Monday, 9 September 2019 12:33:37 UTC-4, peteolcott wrote:
>> On 9/9/2019 10:57 AM, Fred wrote:
>>> On 09/09/2019 15:38, peteolcott wrote:
>>>> On 9/8/2019 9:33 AM, Fred wrote:
>>>>> On 07/09/2019 20:10, Fred wrote:
>>>>>> On 07/09/2019 19:49, peteolcott wrote:
>>>>>>> On 9/7/2019 12:27 PM, Fred wrote:
>>>>>>>> On 07/09/2019 18:11, peteolcott wrote:
>>>>>>>>
>>>>>>>>> When the principle of explosion [reasons past the contradiction] it makes
>>>>>>>>> mathematical logic inconsistent because the same contradiction that proves
>>>>>>>>
>>>>>>>> The same contradiction that *proves*...  I.e., you're starting with a contradiction *not* deducing one.  Deduce A&~A from (whatever you mean by) mathematical logic.  You can't.  You don't even know that that's what you need to do to show something
>>>>>>>> inconsistent.
>>>>>>>>
>>>>>>>
>>>>>>> We simply form an inference chain of Reductio ad absurdum with the
>>>>>>
>>>>>> If it's simple, do it!  Start with Mendelson's propositional calculus and prove A and ~A as theorems, for some formula A.
>>>>>>
>>>>>>> principle of explosion.
>>>>>>> Rules-of-inference can be chained right?
>>>>>>>
>>>>>>> Proposition Y derives contradiction X proving that Y is false.
>>>>>>> Proposition Y derives contradiction X applied to the Principle of Explosion proving that Y is true.
>>>>>>> Therefore Y is false and Y is true unless we reject POE as a valid rule-of-inference.
>>>>>>
>>>>>> POE and RAA are derived rules of Mendelson's PC.
>>>>>
>>>>> The soundness of PC is the easiest metaproof in the whole of logic.
>>>>> The axioms are all tautologies.  The rule of inference transmits tautologousness.  Therefore the theorems are all tautologies.
>>>>>
>>>>
>>>> All of mathematical logic works this same way. ONLY incorrect reasoning
>>>
>>> Try not to change the subject.  The idea that you know anything about *all* of mathematical logic is preposterous.
>

> This is a common fallacy of argument by authority. I don't have to know *anything* about a particular topic in order to realise there is a discrepancy in the material which I study. I am not inferior intellectually to anyone on the planet which means I don't need years of study to realise what mainstream baboons never realise in a lifetime. The retort is usually a flavour ala Zelos Malum: "I am far more educated than you."
>
> Chuckle. When all else fails for a cranky mainstream academic, simply resort to the authority bestowed by the Church of Academia.
>

Sure. If the body of mathematical knowledge is very large and one
hardly knows much of any of the details of this body of knowledge
one could still detect a fundamental architectural flaw that forms
the basis of this body, for example:

THIS IS A COMPLETE REFUTATION OF THE 1931 INCOMPLETENESS THEOREM
Conceptual truth is always provable because the same relations
between expressions of language that define the truth of an
expression also define the proof of this same expression.

> I would never have discovered the New Calculus if I didn't immediately see numerous problems with mainstream knowledge which in this case I studied longer and harder than anyone I know!

[peteolcott]

On 9/10/2019 6:42 AM, Eram semper recta wrote:

> On Saturday, 7 September 2019 18:08:41 UTC-4, peteolcott wrote:
>> On 9/7/2019 4:45 PM, David Petry wrote:
>>>
>>>
>>> peteolcott wrote:
>>>
>>>> Conceptual truth is a set of mutually self-defining interlocking semantic tautologies.
>>>
>>>> Conceptual truth is a set of relations between finite strings defined to have the semantic property of Boolean True.
>>>
>>>
>>> FWIW, that really doesn't clarify things for me.
>>>
>>
>> You know how the operation of arithmetic works on strings of numeric digits right?
>> "2 + 3 = 5" is true and provable on the basis of the algorithm that defines the
>> relations in that string. "2 + 3" is defined to have an "=" relation to "5".
>> In philosophy of math it is said that "2 + 3" satisfies the "=" relation to "5".
>> All conceptual truth works this same way.
>>
>> "cats" are defined to have the "type of" relation to "animals".
>> The entire set of conceptual truth can for formalized as these same
>> relations between finite strings.
>>
>> There is never a case where a conceptual truth cannot be formalized
>> as a relation between finite strings, thus refuting Tarski Undefinability.
>> There is never a case where the satisfaction of these relations does
>> not concurrently specify provability and truth, thus refuting 1931
>> Incompleteness.
>

> Good stuff Pete. I am glad there is someone like you refuting all this nonsense given that you have studied it extensively and it shows! Although I have done a lot of reading, to be frank, I have never cared to spend more effort than was necessary because I normally abandon theory at the first occasion where I see it fails.
>
> I don't have your knowledge of set theory or logic.
>
Thanks for the support

I have known all these things for at least thirty years.
I only briefly skim the work of others to obtain the
terminology for expressing these things that I have always known.

Here is Wittgenstein's one page simple English refutation of Gödel:
http://liarparadox.org/Wittgenstein.pdf

[peteolcott]

On 9/10/2019 12:09 AM, André G. Isaak wrote:
> On 2019-09-09 10:51 p.m., peteolcott wrote:
>> On 9/9/2019 11:25 PM, André G. Isaak wrote:
>>> On 2019-09-09 9:39 p.m., peteolcott wrote:
>>>> On 9/9/2019 10:25 PM, André G. Isaak wrote:
>>>>> On 2019-09-09 9:13 p.m., peteolcott wrote:
>>>>>> On 9/9/2019 10:05 PM, André G. Isaak wrote:
>>>>>>> On 2019-09-09 8:37 p.m., peteolcott wrote:
>>>>>>>> On 9/9/2019 9:12 PM, André G. Isaak wrote:
>>>>>>>>> On 2019-09-09 3:49 p.m., peteolcott wrote:
>>>>>>>>>> On 9/9/2019 3:59 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2019-09-09 2:47 p.m., peteolcott wrote:
>>>>>>>>>>>> On 9/9/2019 2:03 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2019-09-09 12:52 p.m., peteolcott wrote:
>>>>>>>>>>>>>> On 9/9/2019 1:23 PM, Fred wrote:

>>>>>>>>>>>>>>> Consider
>>>>>>>>>>>>>>> i) for all natural numbers x and y, xy = yx;
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://www.analyzemath.com/algebra/rules_algebra.html
>>>>>>>>>>>>>> 2. Commutative Property of Multiplication.
>>>>>>>>>>>>>> a × b = b × a
>>>>>>>>>>>>>
>>>>>>>>>>>>> How does this answer the question? Yes, multiplication is normally commutative, but that tells us nothing about how you derive this as a relation between finite strings.
>>>>>>>>>>>>>
>>>>>>>>>>>>>>> ii) there are natural numbers x and y such that xy =/= yx.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> What the Hell does =/= mean?
>>>>>>>>>>>>>
>>>>>>>>>>>>> It doesn't take a genius to figure out that that is an ASCII rendering of ≠, especially given that this is entirely clear from the context.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> What does it take to believe that there are exceptions to this rule?
>>>>>>>>>>>
>>>>>>>>>>> Stating there are no exceptions to this rule and proving that there are no exceptions to this rule are entirely different things.
>>>>>>>>>>>
>>>>>>>>>>> How do you manipulate your finite strings in order to prove this?
>>>>>>>>>>>
>>>>>>>>>>>> https://www.analyzemath.com/algebra/rules_algebra.html
>>>>>>>>>>>> 2. Commutative Property of Multiplication.
>>>>>>>>>>>> a × b = b × a
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> They are the logical opposites of one another.  What relations between finite strings makes which one true?

>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I clarified this formalist perspective and provided the next level of
>>>>>>>>>>>>>>>

>>>>>>>>>>>>>>> You have clarified *nothing*.  You have never read what any formalist said about anything.  You cannot even name a handful of formalists.
>>>>>>>>>>>>>>> Correction (maybe): perhaps you have read (and quoted here) a couple of sentences from one formalist.  But not read and quoted with understanding, so it hardly counts.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You do not seem very good at the gist of things:
>>>>>>>>>>>>>> (This is 100% of the entire whole complete essence of the mathematical formalist school)
>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics)
>>>>>>>>>>>>>> In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings...
>>>>>>>>>>>>>
>>>>>>>>>>>>> So what manipulation of strings allows you to derive "for all natural numbers x and y, xy = yx"?
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So you believe that axioms are derived rather than specified?
>>>>>>>>>>>
>>>>>>>>>>> Commutativity is provable in PA without the addition of an axiom.
>>>>>>>>>>>
>>>>>>>>>>> I'm asking you what the string manipulation involved in proving this theorem is.
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> None of you can begin understand these things beyond your learned-by-rote memorization.
>>>>>>>>>>
>>>>>>>>>> The degree of detail that you are asking for totally misses the whole point of
>>>>>>>>>> specifying the philosophical underpinnings of the formalist school of mathematical proofs.
>>>>>>>>>>
>>>>>>>>>> We don't go through every tiny little detail one at a time.
>>>>>>>>>
>>>>>>>>> Pretty much all formalists would disagree with the above given that formalists tend to be rather details-oriented.
>>>>>>>>>
>>>>>>>>>> Once we find that no category exists that refutes the assertion
>>>>>>>>>> WE ARE 100% TOTALLY COMPLETELY ALL-THE-WAY DONE!
>>>>>>>>>
>>>>>>>>> You haven't shown an 'category' which exists that actually supports your assertions. You seem to have a bass-akwards notion of how burden of proof operates.
>>>>>>>>>
>>>>>>>>>> Categorically exhaustively reasoning never delves into any details
>>>>>>>>>> deeper than a category.
>>>>>>>>>
>>>>>>>>> This has to be among the silliest statements that you'd made.
>>>>>>>>>
>>>>>>>>> It's as if Newton had asserted that all of physics could be described by mathematical relations between physical quantities, but then stopped there because things like 'F=ma' or F_g = Gm_1m_2/r^2 are just tedious details and we should never delve
>>>>>>>>> into those.
>>>>>>>>
>>>>>>>> My problem is that most philosophers are are totally clueless about math
>>>>>>>> and most mathematicians can only think of things in terms of what they
>>>>>>>> learned-by-rote and thus misconstrue all news ideas that are outside of
>>>>>>>> the box of what they learned-by-rote as incorrect.
>>>>>>>>
>>>>>>>> You are obviously totally clueless about the analytic/ synthetic distinction
>>>>>>>> or you would not brought up Newtons work because you would know that it is
>>>>>>>> in the wrong basic category.
>>>>>>>
>>>>>>> Clearly, you don't understand how analogies work.
>>>>>>
>>>>>> Categorical investigation is only ensured to work on the analytical
>>>>>> side of the analytic synthetic distinction, thus the progressively
>>>>>> increasing specificity of Categorical investigation is wholly inappropriate
>>>>>> for synthetic knowledge.
>>>>>
>>>>> As far as I can tell, the above sentence doesn't actually mean anything (especially considering the fact that you don't understand what 'analytic' means). What exactly is the 'progressively increasing specificity of Categorical Investigation"? And
>>>>> where in your 'work' do we actually find anything which might be described as 'increasing specificity' given that you avoid all details.
>>>>>
>>>>>> You don't really care about any of this stuff,
>>>>>
>>>>> If I didn't care about it, why would I bother posting about it?
>>>>>
>>>>
>>>> The question isn't why do I bother posting it.
>>>
>>> That's also not the question I asked.
>>>
>>>> I bother posting it so that I have a proven continuous stream
>>>> of copyright protection for each increment of my innovative new ideas.
>>>
>>> That's not what usenet is for. Usenet is a discussion forum. If you're not interested in discussing, then your posts don't belong here.
>>>
>>> If you just want to prove copyright, write your ideas down on a napkin and mail them to yourself.
>>>
>>
>> That is not how it actually works. USENET is actually the best forum for this purpose.
>
> Then you need to brush up on copyright law. As soon as something is put into a tangible form, copyright is attached. All you need for proof of copyright is something which attaches a date to your work.

The postal mail patent does not work because you could send yourself an
unsealed envelope and many years later seal something inside it.
For patents someone must have read and understood your invention
to be an effective witness of its creation date. This is all made
mostly moot now that the USA has moved from first to invent to first
to file a patent.

To prove that an idea actually was created on a certain date it is
best that this idea was actually published on this date, USENET
counts as publication.


>
>>>> The question is why do I keep responding to people that have no actual
>>>> interest in an honest dialogue.
>>>
>>> 'Honest Dialogue' requires that you actually answer questions about your alleged system. Why not start with the one below?
>>>
>>>>>> Just like everyone else
>>>>>> you only pursue the single-minded goal of Pete must be wrong because
>>>>>> you really really believe that Pete must be wrong.
>>>>>
>>>>> On the contrary, I don't think you are wrong. To be wrong, you would have to had made some claim which was sufficiently precise to actually be evaluated. Your claims are all far to vague to be categorized as 'right' or 'wrong'.
>>>>>
>>>>> If you want to show you are right, you can start by providing an explanation for how, according to you, the manipulation of finite strings can demonstrate the commutativity of addition. What are the rules of manipulation which are permitted? Without
>>>>> specifying these rules, 'manipulation of finite strings' could mean absolutely anything.
>>>
>>> I.e. this question ↑
>>
>> I already explained this: axioms, rules-of-inference, axiom schemata
>> to algorithmically compress infinite sets of axioms.
>
> This isn't an explanation unless you actually specify some axioms and describe your rules of inference.

What the Hell you are totally clueless about what axioms and rules-of-inference are?
If this is the case you have no business responding to any of my posts.

>
> Demonstrating your axioms and rules of inference with an *actual example*, such as proving the above statement would minimally be a start. Unless you answer this, I have to conclude that you don't actually have a set of inference rules which can actually
> demonstrate this.
>

I have no time for tutorial.

>> Fred / Peter Percival makes it a game to ask the same question
>> make sure to ignore the answer and then ask the same question
>> again over and over ad infinitum.
>
> That's because you have never actually answered it. Talking about 'rules of inference' without providing any rules of inference isn't an answer.
>

If you are claiming that I need to explain what rules-of-inference are you
must be a damn liar. Quit your damn lying damn liar !!!

>>>
>>>>>>> In the above case the relevant point being compared was the lack of detail.
>>>>>>>
>>>>>>> As for the analytic/synthetic distinction, to the extent that this distinction is even well-defined (an issue which you would be familiar with had you actually read any of the literature), your view of this distinction seems to bear little
>>>>>>> resemblance to its use by those who actually proposed this distinction since you seem to treat all sorts of things as 'analytic' which few others would (e.g. 'Cats are mammals', '2+2=4').
>>>
>>> You might also want to explain what you mean by 'analytic'
>>
>> It is a common term from philosophy, look it up.
>
> I am quite familiar with what it means.
>
>>> such that it ends up including sentences like 'Cats are Mammals' or '2 + 2 = 4'. Then you might want to discuss why your distinction doesn't bear any resemblance to the one posited by e.g. Kant. And since Kant has priority here, if you want to discuss
>>> some other distinction you should pick a different name. Do you simply mean _a priori_ or do you mean something else?
>>>
>>
>> What I mean (as I have told you several times already) is analytic is
>> every detail of knowledge that can be totally defined entirely on the
>> basis of the meaning of its words, and synthetic is those aspects of
>> knowledge that require input from the sense organs.
>
> Which isn't how analytic is normally defined.
>

Yes it defines it such that Quine's objections become impossible.

>> It is the same general notion idea as analytic/synthetic a priori/a posteriori
>
> 'a priori' and 'analytic' are not the same thing. So which is it?
>

It is the gist of the idea of analytic/synthetic and a priori/a posteriori
expressing this gist a little more precisely.

>> with perhaps just enough sharper focus to totally eliminate Quine's
>> objections.
>
> You haven't read Quine so how can you claim this?
>

I skimmed what he said enough to know that his objection does not
and cannot address my definition.

>> Copyright 2019 Pete Olcott
>>
>>> Have you actually read the First Critique?
>
> No answer? If you're going to go on about the analytic/synthetic distinction, this is certainly something you ought to have read. It's been translated to English multiple times. The Guyer and Wood translation is decent, as is Pluhar. Acting as if you are
> an expert on some topic when you haven't even read any of the primary literature on the topic is markedly dishonest.
>

I don't have to read all of the misconceptions of others to use categorically
exhaustive reasoning to progressively deduce the ultimate truth of these things.

Instead of asking silly questions to indirectly assess how much of the misconceptions
of others that I have encountered (this is only a measure of credibility, not validity),

Try to find actual flaws in what I have said and thus directly examine the validity of what I said.

When we use my division of the analytic/synthetic distinction
then THIS BECOMES A COMPLETE REFUTATION OF THE 1931 INCOMPLETENESS THEOREM:

Conceptual truth is always provable because the same relations
between expressions of language that define the truth of an
expression also define the proof of this same expression.

Once the above is completely understood it is understood to refute Gödel.

>>> Have you read the criticisms put forth by Quine and others? [By this I mean the actual papers, not a summary in an encyclopaedia].
>
> Ditto.
>
>>> If you use terms in a manner other than the commonly accepted one, how exactly is it that you expect people to understand what it is that you are claiming?
>>>
>>> André >
>>>>>>> You really should read Kant's First Critique in which he lays out this terminology and in which he contrasts it with _a priori_ and _a posteriori_. You seem to treat 'analytic' as being a synonym for 'a priori'. It isn't.
>>>>>>>
>>>>>>> Once you've finished reading Kant, you should actually read Quine rather than simply reading encylopaedia articles about him. The relevant paper ("Two Dogmas of Empiricism") is relatively short.
>>>>>>>
>>>>>>> André

[peteolcott]

On 9/10/2019 10:33 AM, Fred wrote:

> On 10/09/2019 03:37, peteolcott wrote:
>
>
>> My problem is that most philosophers are are totally clueless about math
>> and most mathematicians can only think of things in terms of what they
>> learned-by-rote and thus misconstrue all news ideas that are outside of
>> the box of what they learned-by-rote as incorrect.
>

> You, on the other hand, have a considerable knowledge of mathematics and philosophy.  Is that your claim?  What are your qualifications in those two fields?  Don't be modest, do tell.
>
>

I ONLY need a sufficient knowledge of the intersection of mathematics
and philosophy to derive very significant new insights within this
intersection.

Although the gist of my ideas have proven to have always been correct
the key aspect from mathematics that I was missing is a sufficient
understanding of the conventional meaning of the terms of the art.

I had to go about learning these terms in an enormously clumsy way
because I knew that some fundamental error was directly encoded into
conventional wisdom. I initially suspected that subtle error was directly
encoded into the definitions of the terms of the art. This is why I
flailed around like a fish out-of-water using these terms as mere
approximations of what I was saying without being able to explicitly
refine the distinctions between my meaning and the conventional meaning.

In order to communicate the most effectively I had to use the conventional
terms of the art with their conventional meanings to define my new ideas.

THIS IS THE SIMPLEST POSSIBLE REFUTATION OF 1931 INCOMPLETENESS

Conceptual truth is always provable because the same relations
between expressions of language that define the truth of an
expression also define the proof of this same expression.

[peteolcott]

On 9/10/2019 11:29 AM, Fred wrote:

> On 10/09/2019 16:57, peteolcott wrote:
>> On 9/10/2019 10:33 AM, Fred wrote:
>>> On 10/09/2019 03:37, peteolcott wrote:
>>>
>>>
>>>> My problem is that most philosophers are are totally clueless about math
>>>> and most mathematicians can only think of things in terms of what they
>>>> learned-by-rote and thus misconstrue all news ideas that are outside of
>>>> the box of what they learned-by-rote as incorrect.
>>>
>>> You, on the other hand, have a considerable knowledge of mathematics and philosophy.  Is that your claim?  What are your qualifications in those two fields?  Don't be modest, do tell.
>>>
>>>
>>
>> I ONLY need a sufficient knowledge of the intersection of mathematics
>> and philosophy to derive very significant new insights within this
>> intersection.
>

> Ok, what knowledge do you have of the intersection of mathematics and philosophy?  What are the sources of your knowledge?


I figured out that this is self-evidently correct:

[peteolcott]

On 9/10/2019 1:04 PM, Fred wrote:

> On 09/09/2019 22:49, peteolcott wrote:
>> On 9/9/2019 3:59 PM, André G. Isaak wrote:
>
>
>>> Commutativity is provable in PA without the addition of an axiom.
>>>
>>> I'm asking you what the string manipulation involved in proving this theorem is.
>>>
>>> André
>>
>>
>> None of you can begin understand these things beyond your learned-by-rote memorization.
>>
>> The degree of detail that you are asking for totally misses the whole point of
>> specifying the philosophical underpinnings of the formalist school of mathematical proofs.
>>
>> We don't go through every tiny little detail one at a time.
>

> You've never gone through any detail.  In fact you've never done anything.  You, after much messing about, produced the grammar of MTT, but you've never specified one axiom or rule of it.
>

Try and find any exception to the rule where conceptual truth
is not concurrently specified with its provability on the basis
of the satisfaction of relations between finite strings.

These finite strings are comprised of:
(a) axioms
(b) rules-of-inference
(c) Axiom schemata algorithmically compressing otherwise infinite sets of axioms.

https://en.wikipedia.org/wiki/Switcheroo
Both Gödel and Tarski use a fallacy of equivocation switcheroo.
We know its true over here because its provable over there.

> Pick your preferred relevance logic, add some arithmetic of axioms to it, and prove some fact of arithmetic.  You don't even know how to begin.
>
> Do you think you fool anyone?

>
>>
>> Once we find that no category exists that refutes the assertion
>> WE ARE 100% TOTALLY COMPLETELY ALL-THE-WAY DONE!
>>

>> Categorically exhaustively reasoning never delves into any details
>> deeper than a category.
>
>
>

[peteolcott]

On 9/10/2019 11:46 AM, Eram semper recta wrote:

> On Tuesday, September 10, 2019 at 10:57:08 AM UTC-4, peteolcott wrote:
>
>> THIS IS A COMPLETE REFUTATION OF THE 1931 INCOMPLETENESS THEOREM
>
>> Conceptual truth is always provable because the same relations
>> between expressions of language that define the truth of an
>> expression also define the proof of this same expression.
>

> To me, the phrase "conceptual truth" is a redundancy. 'Truth' is that conceptual knowledge which is in agreement with *facts*. So, truth is always provable because of facts that provide the evidence required in order to be convinced of the truth being perceived.
>


I define the analytic/synthetic distinction differently thus overcoming
Quine's objections: Analytic is every detail of knowledge that can be totally

defined entirely on the basis of the meaning of its words, and synthetic is
those aspects of knowledge that require input from the sense organs.

Copyright 2019 Pete Olcott

When I refer to conceptual, I am referring tot he synthetic defined above.

That is Bill over there. I know him because I remember what his face looks like.

> I don't understand what you mean by this part:

>
> "the same relations between expressions of language that define the truth of an expression also define the proof of this same expression."
>

> i. What are the relations between expressions of language?
> ii. The "proof of this same expression" refers to the original truth statement?
>
>

These finite strings (expressions of language) are comprised of:

(a) axioms
(b) rules-of-inference
(c) Axiom schemata algorithmically compressing otherwise infinite sets of axioms.

The same thing applies to all of the facts and rules specified in human languages.

When we know that a cat is an animal and that an animal is a living thing
we can correctly infer that a cat is a living thing. The entire body
of conceptual knowledge is specified as relations between expressions of
language such that these relations have been defined to have the semantic
property of Boolean true.

[peteolcott]

On 9/10/2019 3:46 PM, Fred wrote:
> On 10/09/2019 21:35, peteolcott wrote:
>> On 9/10/2019 3:32 PM, Fred wrote:
>>> On 10/09/2019 21:24, peteolcott wrote:
>>>> On 9/10/2019 3:04 PM, Fred wrote:
>>>>> On 10/09/2019 20:54, peteolcott wrote:
>>>>>> On 9/10/2019 2:28 PM, Fred wrote:

>>>>>>> On 10/09/2019 19:38, peteolcott wrote:
>>>>>>>
>>>>>>>
>>>>>>>> I define the analytic/synthetic distinction differently thus overcoming
>>>>>>>

>>>>>>> So when you write of the analytic/synthetic distinction you're not writing about what anyone (including Quine) is saying.

>>>>>>>
>>>>>>>> Quine's objections: Analytic is every detail of knowledge that can be totally
>>>>>>>> defined entirely on the basis of the meaning of its words, and synthetic is
>>>>>>>> those aspects of knowledge that require input from the sense organs.
>>>>>>>> Copyright 2019 Pete Olcott
>>>>>>>>
>>>>>>>> When I refer to conceptual, I am referring tot he synthetic defined above.
>>>>>>>>
>>>>>>>> That is Bill over there. I know him because I remember what his face looks like.
>>>>>>>>
>>>>>>>>> I don't understand what you mean by this part:
>>>>>>>>>
>>>>>>>>> "the same relations between expressions of language that define the truth of an expression also define the proof of this same expression."
>>>>>>>>>
>>>>>>>>> i.   What are the relations between expressions of language?
>>>>>>>>> ii.  The "proof of this same expression" refers to the original truth statement?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> These finite strings (expressions of language) are comprised of:
>>>>>>>> (a) axioms
>>>>>>>> (b) rules-of-inference
>>>>>>>> (c) Axiom schemata algorithmically compressing otherwise infinite sets of axioms.
>>>>>>>

>>>>>>> For example?  Prove just one think on such a basis.

>>>>>>
>>>>>> For example the set of all relations between finite strings of numeric
>>>>>> digits for this relational operator: "=" and this function: "+" is
>>>>>> specified by its corresponding algorithm.
>>>>>
>>>>>

>>>>> Axioms?  Rules-of-inference?  It is you who mentioned them.  Since you mention = and +.  Prove that x+y=y+x for all natural numbers x and y.
>>>>>
>>>>>
>>>>
>>>>
>>>> Why did you lie and say that there was a counter-example to this?
>>>
>>> Please identify the post with Subject header, day and time, when I said there was a counter-example to anything; and please say counter-example to what in this particular case.
>>>
>>> You seem to be loosing touch with reality.  What I have been saying (more than once, I'm sure) is that you have produced nothing for there to be a counter-example to.
>>
>>
>> FIND A COUNTER-EXAMPLE TO THIS
>
> I see the problem.  You don't know what a counter-example is.  If someone claims
>
>   For all x of a certain kind, something P about x is true.
>
> and someone else identifies a y of that kind such that P is false of y, then that someone else has found a counter-example to the claim.  In symbols - given "(forall x)(if K(x) then P(x))" a counter-example to that would be a y such that "K(y) and not
> P(y)".  Most importantly, a counter-example is a counter-example to a *universal* statement.  So if you want a counter-example to something, the something needs to start "forall x..."
>
> For how many years have you been using the term "counter-example" without knowing what it means?
>
> This stands -
> Please identify the post with Subject header, day and time, when I said there was a counter-example to anything; and please say counter-example to what in this particular case.
>
> If you don't do it I'll assume you were lying.

>
>> THIS IS THE SIMPLEST POSSIBLE REFUTATION OF 1931 INCOMPLETENESS

>> Conceptual truth is always provable because the same relations
>> between expressions of language that define the truth of an
>> expression also define the proof of this same expression.
>>

https://en.wikipedia.org/wiki/Counterexample
In logic, and especially in its applications to mathematics and philosophy,
a counterexample is an exception to a proposed general rule or law. For
example, consider the proposition "all students are lazy". Because this
statement makes the claim that a certain property (laziness) holds for all
students, even a single example of a diligent student will prove it false.
Thus, any hard-working student is a counterexample to "all students are lazy".

More precisely, a counterexample is a specific instance of the falsity
of a universal quantification (a "for all" statement).

In other words find any example of any statement that is verified as
completely true entirely based on the meaning of its words

(Or any logic sentence that is verified as true based on its
meaning (such as a tautology))

where this same statement/logic sentence cannot be proven.

[André G. Isaak]

Patent Law has nothing to do with Copyright.

> To prove that an idea actually was created on a certain date it is
> best that this idea was actually published on this date, USENET
> counts as publication.

This doesn't change the fact that this was never an intended function
for usenet.

I can only interpret the above in two possible ways. Either (i) you are
being deliberately obtuse or (ii) you genuinely have no clue what is
being asked.

Different logics have different rules of inference. The rules of
inference associated with propositional calculus are different from the
rules of inference adopted by various 1st order logics which are in turn
different from those in modal logic etc.

I'm not asking you to define "rule of inference". I'm asking you *which*
rules of inference your system accepts as sound. The fact that you
reject POE clearly indicates that you reject at least some rules of
inference of classical logic, but it's not clear which, and therefore
which rules you still accept.

It's not clear which rules of inference of higher order logics you allow
because you've never made it clear *which* logic you are using. In fact
it's not even clear which language you are using since in your
discussions you freely mix the syntax of various logics along with
syntactically ill-formed statements of various logics along with prolog
along with C++ along with the kitchen sink.

Stating that commutativity can be proved using 'axioms and rules of
inference' is completely meaningless unless you state *which* axioms and
*which* rules of inference you are adopting.

To make this clearer, let me make the following claim: I, too, have
invented a system in which everything is expressed as relations between
finite strings and rules which manipulate those strings. However, my
system uses an entirely different set of string-manipulation rules than
yours, and my system is better.

If I ask you to refute the above claim, how can you possibly do this
given that I haven't told you anything about how my system works?

>
>> Demonstrating your axioms and rules of inference with an *actual
>> example*, such as proving the above statement would minimally be a
>> start. Unless you answer this, I have to conclude that you don't
>> actually have a set of inference rules which can actually demonstrate
>> this.
>>
>
> I have no time for tutorial.

Example != Tutorial.

>>> Fred / Peter Percival makes it a game to ask the same question
>>> make sure to ignore the answer and then ask the same question
>>> again over and over ad infinitum.
>>
>> That's because you have never actually answered it. Talking about
>> 'rules of inference' without providing any rules of inference isn't an
>> answer.
>>
>
> If you are claiming that I need to explain what rules-of-inference are you
> must be a damn liar. Quit your damn lying damn liar !!!

No one is asking you to explain what rules of inference are[1]. We are
asking you to state *which* rules of inference you are adopting.


[1] or if they are it is only to confirm that you have absolutely no
idea what they are. Hint: Cat(x) -> Mammal(x) may be a rule of prolog,
but it is *not* a rule of inference.

>>>>
>>>>>>>> In the above case the relevant point being compared was the lack
>>>>>>>> of detail.
>>>>>>>>
>>>>>>>> As for the analytic/synthetic distinction, to the extent that
>>>>>>>> this distinction is even well-defined (an issue which you would
>>>>>>>> be familiar with had you actually read any of the literature),
>>>>>>>> your view of this distinction seems to bear little resemblance
>>>>>>>> to its use by those who actually proposed this distinction since
>>>>>>>> you seem to treat all sorts of things as 'analytic' which few
>>>>>>>> others would (e.g. 'Cats are mammals', '2+2=4').
>>>>
>>>> You might also want to explain what you mean by 'analytic'
>>>
>>> It is a common term from philosophy, look it up.
>>
>> I am quite familiar with what it means.
>>
>>>> such that it ends up including sentences like 'Cats are Mammals' or
>>>> '2 + 2 = 4'. Then you might want to discuss why your distinction
>>>> doesn't bear any resemblance to the one posited by e.g. Kant. And
>>>> since Kant has priority here, if you want to discuss some other
>>>> distinction you should pick a different name. Do you simply mean _a
>>>> priori_ or do you mean something else?
>>>>
>>>
>>> What I mean (as I have told you several times already) is analytic is
>>> every detail of knowledge that can be totally defined entirely on the
>>> basis of the meaning of its words, and synthetic is those aspects of
>>> knowledge that require input from the sense organs.
>>
>> Which isn't how analytic is normally defined.
>>
>
> Yes it defines it such that Quine's objections become impossible.

IOW it defines it such that you are not talking about the same thing
that Quine, or Kant, or any other philosopher of language is talking about.

>>> It is the same general notion idea as analytic/synthetic a priori/a
>>> posteriori
>>
>> 'a priori' and 'analytic' are not the same thing. So which is it?
>>
>
> It is the gist of the idea of analytic/synthetic and a priori/a posteriori
> expressing this gist a little more precisely.

No one here cares about 'gists'. We care about precise definitions.

>>> with perhaps just enough sharper focus to totally eliminate Quine's
>>> objections.
>>
>> You haven't read Quine so how can you claim this?
>>
>
> I skimmed what he said enough to know that his objection does not
> and cannot address my definition.
>
>>> Copyright 2019 Pete Olcott
>>>
>>>> Have you actually read the First Critique?
>>
>> No answer? If you're going to go on about the analytic/synthetic
>> distinction, this is certainly something you ought to have read. It's
>> been translated to English multiple times. The Guyer and Wood
>> translation is decent, as is Pluhar. Acting as if you are an expert on
>> some topic when you haven't even read any of the primary literature on
>> the topic is markedly dishonest.
>>
>
> I don't have to read all of the misconceptions of others to use
> categorically
> exhaustive reasoning to progressively deduce the ultimate truth of these
> things.

You do need to read the works of others to understand what philosophical
terminology actually means in order to effectively communicate with others.

> Instead of asking silly questions to indirectly assess how much of the
> misconceptions
> of others that I have encountered (this is only a measure of
> credibility, not validity),
>
> Try to find actual flaws in what I have said and thus directly examine
> the validity of what I said.
> When we use my division of the analytic/synthetic distinction
> then THIS BECOMES A COMPLETE REFUTATION OF THE 1931 INCOMPLETENESS THEOREM:
>
> Conceptual truth is always provable because the same relations
> between expressions of language that define the truth of an
> expression also define the proof of this same expression.
>
> Once the above is completely understood it is understood to refute Gödel.

No one can provide a refutation of the above because it doesn't actually
make a claim. Talking about 'relations between expressions' doesn't say
anything unless you describe what those relations actually are and how
'proofs' actually work in this system.

Let's say I claim to have a invented a new boardgame which is more
challenging and fun than any other boardgame. This game works by using
rules which govern how pieces may move on the board.

Does the above description tell you anything whatsoever about how this
game works? No. Your alleged 'system' is exactly the same as the above.
You talk about rules of inference and axioms but make absolutely not
attempt to discuss the actual content of those rules and axioms leaving
the reader with absolutely no information about your system.

André




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

[peteolcott]

Perhaps I need to reiterate exactly what a higher level of abstraction is.
I am talking about the basic architecture that concurrently applies to
every formal system. I am not proceeding beyond this high level abstraction
to any additional elaboration. I can't tell you all of these details
because they vary and I am not referring to their variance only their
commonality.

We can see that in any natural language system that the truth of any
expression of conceptual knowledge only depends upon the meaning of
the words of this expression.

This same idea equally applies to formal systems. The truth of any
expression of language only depends on the compositional meaning of
this expression.

**Conceptual knowledge:
All knowledge that does not require any input from the sense organs
to verify its truth.

[André G. Isaak]

Without these additional elaborations, though, your claims end up being
entirely vaccuous.

And you are not in a position to talk about every formal system, since
there are a great many formal systems out there which you are not
familiar with.

> We can see that in any natural language system that the truth of any
> expression of conceptual knowledge only depends upon the meaning of
> the words of this expression.

You might be able to see this. I, however, do not.

The truth of an expression depends on the meaning of the words, yes, but
it also depends upon the syntactic and semantic rules of the language.
And representing the meaning of words in natural language is a
non-trivial matter which is the subject of huge amounts of research in
both linguistics and psychology, absolutely none of which you are even
remotely familiar with.

> This same idea equally applies to formal systems. The truth of any
> expression of language only depends on the compositional meaning of
> this expression.
>
> **Conceptual knowledge:
> All knowledge that does not require any input from the sense organs
> to verify its truth.

Which effectively rules out making claims about the world at all. Truths
which do not require any input from the sense organs essentially limits
you to talking about mathematics and logical tautologies. Claims like
'cats are mammals' or 'cats are not office-buildings' (two of your
favourites) would be excluded.

[peteolcott]

So you are unable to comprehend the concept of a common architecture
across every formal system? Every formal system is specified using
finite strings. Every formal system expresses relations between these
finite strings. Since this seems so simple to me I can't see how this
degree of specificity in unclear to you.

>> We can see that in any natural language system that the truth of any
>> expression of conceptual knowledge only depends upon the meaning of
>> the words of this expression.
>
> You might be able to see this. I, however, do not.

Try to think of every (conceptual) declarative sentence that you have ever seen.
Are there any of these sentences that can be verified as true by any other means
than their meaning?

Is there a magic fairy that taps you on the head thus forming the criterion measure of Truth?
Do you get a little tingling in your chest indicating the truth of a conceptual sentence?
What other ways can we verify that a sentence is factual besides its meaning?

>
> The truth of an expression depends on the meaning of the words, yes, but it also depends upon the syntactic and semantic rules of the language. And representing the meaning of words in natural language is a non-trivial matter which is the subject of huge
> amounts of research in both linguistics and psychology, absolutely none of which you are even remotely familiar with.
>

Ultimately the truth of every natural or formal language sentence boils
down to is compositional meaning.

*** NOTE *** By compositional meaning of natural language sentences I am
expressly including discourse context, most linguists do not.

>> This same idea equally applies to formal systems. The truth of any
>> expression of language only depends on the compositional meaning of
>> this expression.
>>
>> **Conceptual knowledge:
>> All knowledge that does not require any input from the sense organs
>> to verify its truth.
>
> Which effectively rules out making claims about the world at all. Truths which do not require any input from the sense organs essentially limits you to talking about mathematics and logical tautologies. Claims like 'cats are mammals' or 'cats are not
> office-buildings' (two of your favourites) would be excluded.
>
> André
>

Not at all. "I saw Bill walk across the floor" would be excluded.
"Bill walked across the floor" could be construed as a geometric "given".

World knowledge is not ultimately excluded, it is only excluded for
now to reduce the complexity of the analysis.

[David Kleinecke]

Dunno. All plurals are sets and all the machinery of set
theory is available to us.

[André G. Isaak]

But this 'common architecture' is entirely devoid of useful content.
Claiming that formal systems make use of strings tells us absolutely
nothing which constrains the class of formal systems beyond what we
already know, so this contributes no useful information about what
counts as a formal system.

>>> We can see that in any natural language system that the truth of any
>>> expression of conceptual knowledge only depends upon the meaning of
>>> the words of this expression.
>>
>> You might be able to see this. I, however, do not.
>
> Try to think of every (conceptual) declarative sentence that you have
> ever seen.
> Are there any of these sentences that can be verified as true by any
> other means
> than their meaning?

'Cats are mammals', which I believe you consider to be 'conceptual
knowledge' is verified by observation, not by the meanings of the words.

The only things which can be verified solely based on the meanings of
the words are tautologies such as 'Either Fido is a cat or Fido is not a
cat' in which case it is only the meanings of the connectives which is
being considered.

> Is there a magic fairy that taps you on the head thus forming the
> criterion measure of Truth?
> Do you get a little tingling in your chest indicating the truth of a
> conceptual sentence?
> What other ways can we verify that a sentence is factual besides its
> meaning?

We verify it based on whether its meaning conforms to observation. The
meaning alone is insufficient except in very rare instances such as
claims about mathematics.

>>
>> The truth of an expression depends on the meaning of the words, yes,
>> but it also depends upon the syntactic and semantic rules of the
>> language. And representing the meaning of words in natural language is
>> a non-trivial matter which is the subject of huge amounts of research
>> in both linguistics and psychology, absolutely none of which you are
>> even remotely familiar with.
>>
>
> Ultimately the truth of every natural or formal language sentence boils
> down to is compositional meaning.
>
> *** NOTE *** By compositional meaning of natural language sentences I am
> expressly including discourse context, most linguists do not.

OK. So add 'compositional' to the list of terms you don't understand.
Linguists don't include 'discourse context' in compositional meaning,
because that's not what 'compositional' means.

Maybe you can define 'compositional' for us in a way where 'discourse
context' can be involved.

>>> This same idea equally applies to formal systems. The truth of any
>>> expression of language only depends on the compositional meaning of
>>> this expression.
>>>
>>> **Conceptual knowledge:
>>> All knowledge that does not require any input from the sense organs
>>> to verify its truth.
>>
>> Which effectively rules out making claims about the world at all.
>> Truths which do not require any input from the sense organs
>> essentially limits you to talking about mathematics and logical
>> tautologies. Claims like 'cats are mammals' or 'cats are not
>> office-buildings' (two of your favourites) would be excluded.
>>
>> André
>>
>
> Not at all. "I saw Bill walk across the floor" would be excluded.
> "Bill walked across the floor" could be construed as a geometric "given".

What is a 'geometric given'?

André

> World knowledge is not ultimately excluded, it is only excluded for
> now to reduce the complexity of the analysis.
>


--

[peteolcott]

On 9/11/2019 1:08 AM, Zelos Malum wrote:

> Den tisdag 10 september 2019 kl. 13:42:57 UTC+2 skrev Eram semper recta:
>> On Saturday, 7 September 2019 18:08:41 UTC-4, peteolcott wrote:

>>> On 9/7/2019 4:45 PM, David Petry wrote:
>>>>
>>>>
>>>> peteolcott wrote:
>>>>
>>>>> Conceptual truth is a set of mutually self-defining interlocking semantic tautologies.
>>>>
>>>>> Conceptual truth is a set of relations between finite strings defined to have the semantic property of Boolean True.
>>>>
>>>>
>>>> FWIW, that really doesn't clarify things for me.
>>>>
>>>
>>> You know how the operation of arithmetic works on strings of numeric digits right?
>>> "2 + 3 = 5" is true and provable on the basis of the algorithm that defines the
>>> relations in that string. "2 + 3" is defined to have an "=" relation to "5".
>>> In philosophy of math it is said that "2 + 3" satisfies the "=" relation to "5".
>>> All conceptual truth works this same way.
>>>
>>> "cats" are defined to have the "type of" relation to "animals".
>>> The entire set of conceptual truth can for formalized as these same
>>> relations between finite strings.
>>>
>>> There is never a case where a conceptual truth cannot be formalized
>>> as a relation between finite strings, thus refuting Tarski Undefinability.
>>> There is never a case where the satisfaction of these relations does
>>> not concurrently specify provability and truth, thus refuting 1931
>>> Incompleteness.
>>

>> Good stuff Pete. I am glad there is someone like you refuting all this nonsense given that you have studied it extensively and it shows! Although I have done a lot of reading, to be frank, I have never cared to spend more effort than was necessary because I normally abandon theory at the first occasion where I see it fails.
>>
>> I don't have your knowledge of set theory or logic.
>>
>>>

>>> --
>>> Copyright 2019 Pete Olcott All rights reserved
>>>
>>> "Great spirits have always encountered violent
>>> opposition from mediocre minds." Albert Einstein
>

> Neither does he, but neither of you got knoweldge in anything
>

I have sufficient knowledge of the intersection between philosophy and
mathematics for the specific point at hand. When examining formal systems
from the formalist school they are all comprised of relations between
finite strings such that both true and provable are defined concurrently
as the satisfaction of sequences of these relations.

Whether a cat is an animal or 5 > 3, every true statement is always
provable by the same process used to show that it is true and any
statement that cannot be proved does not count as true.

https://en.wikipedia.org/wiki/Switcheroo
Both Gödel and Tarski use a fallacy of equivocation switcheroo:

We know its true over here because its provable over there.

[peteolcott]

Yes that is exactly right, he goofed on that one and
for the exact reasons that you said.

[peteolcott]

On 9/11/2019 3:53 AM, Julio Di Egidio wrote:

> On Wednesday, 11 September 2019 10:33:18 UTC+2, André G. Isaak wrote:
>> On 2019-09-10 11:37 p.m., peteolcott wrote:
>
>>> Are there any of these sentences that can be verified as true by any
>>> other means than their meaning?
>>
>> 'Cats are mammals', which I believe you consider to be 'conceptual
>> knowledge' is verified by observation, not by the meanings of the words.
>>
>> The only things which can be verified solely based on the meanings of
>> the words are tautologies such as 'Either Fido is a cat or Fido is not a
>> cat' in which case it is only the meanings of the connectives which is
>> being considered.
>

> No bachelor is married is an analytic truth, i.e. logically necessary,
> indeed by the meaning of the words. Same goes for cats are mammals.
>
> You too at best don't know what you are talking about.
>
> Julio
>

Yes you are exactly right about this.

[André G. Isaak]

Um, no. I didn't.

All nouns are sets. That has no bearing on what I said. Some sets, like
the set of natural numbers, can be defined without reference to
empirical facts. The sets of buildings or cats or mammals are not among
these sets. Membership in these sets is determined by empirical observation.

[peteolcott]

So you don't know anything about inheritance hierarchies?
A base class specifies all of the commonality of its derived classes.
Cats and dogs have the common properties of all animals.

> Claiming that formal systems make use of strings tells us absolutely nothing which constrains the class of formal systems beyond what we already know, so this contributes no useful
> information about what counts as a formal system.

You flat out ignored the rest of what I said.
RELATIONS BETWEEN FINITE STRINGS.
"cats are animals" "are" means <is a type of>
"2 + 3 = 5" Equality relation

>
>>>> We can see that in any natural language system that the truth of any
>>>> expression of conceptual knowledge only depends upon the meaning of
>>>> the words of this expression.
>>>
>>> You might be able to see this. I, however, do not.
>>
>> Try to think of every (conceptual) declarative sentence that you have ever seen.
>> Are there any of these sentences that can be verified as true by any other means
>> than their meaning?
>
> 'Cats are mammals', which I believe you consider to be 'conceptual knowledge' is verified by observation, not by the meanings of the words.
>

Two other people proved you wrong about this.

> The only things which can be verified solely based on the meanings of the words are tautologies such as 'Either Fido is a cat or Fido is not a cat' in which case it is only the meanings of the connectives which is being considered.
>
>> Is there a magic fairy that taps you on the head thus forming the criterion measure of Truth?
>> Do you get a little tingling in your chest indicating the truth of a conceptual sentence?
>> What other ways can we verify that a sentence is factual besides its meaning?
>
> We verify it based on whether its meaning conforms to observation. The meaning alone is insufficient except in very rare instances such as claims about mathematics.
>
>>>
>>> The truth of an expression depends on the meaning of the words, yes, but it also depends upon the syntactic and semantic rules of the language. And representing the meaning of words in natural language is a non-trivial matter which is the subject of
>>> huge amounts of research in both linguistics and psychology, absolutely none of which you are even remotely familiar with.
>>>
>>
>> Ultimately the truth of every natural or formal language sentence boils
>> down to is compositional meaning.
>>
>> *** NOTE *** By compositional meaning of natural language sentences I am
>> expressly including discourse context, most linguists do not.
>
> OK. So add 'compositional' to the list of terms you don't understand. Linguists don't include 'discourse context' in compositional meaning, because that's not what 'compositional' means.
>
> Maybe you can define 'compositional' for us in a way where 'discourse context' can be involved.

The asinine linguistic term of compositionality + discourse context.
I could have linked to the Cyc project's Davidson representations but
Cyc erased that fro their website. Once David Kleinecke saw that link
the years long contention regarding compositionality was finally resolved.

Here is the original paper by Davidson:
http://semantics.uchicago.edu/kennedy/classes/s13/aspect/davidson67.pdf
it not not nearly as clear as the Cyc summary of it.

>
>>>> This same idea equally applies to formal systems. The truth of any
>>>> expression of language only depends on the compositional meaning of
>>>> this expression.
>>>>
>>>> **Conceptual knowledge:
>>>> All knowledge that does not require any input from the sense organs
>>>> to verify its truth.
>>>
>>> Which effectively rules out making claims about the world at all. Truths which do not require any input from the sense organs essentially limits you to talking about mathematics and logical tautologies. Claims like 'cats are mammals' or 'cats are not
>>> office-buildings' (two of your favourites) would be excluded.
>>>
>>> André
>>>
>>
>> Not at all. "I saw Bill walk across the floor" would be excluded.
>> "Bill walked across the floor" could be construed as a geometric "given".
>
> What is a 'geometric given'?

A stipulated truth. It is taken to be true even if it is false.

>
> André
>
>> World knowledge is not ultimately excluded, it is only excluded for
>> now to reduce the complexity of the analysis.
>>
>
>


--

[André G. Isaak]

Where does your above claim mention 'inheritance hierarchies'? If this
was intended to be part of your 'common architecture', you would need to
have mentioned this in addition to 'finite strings' and 'relations
between finite strings'.

And given you claim this architecture holds for all formal systems, I
can assure you that 'inheritance hierarchies' cannot be part of it since
most formal systems do not involve any concept of 'inheritance hierarchies'.

> A base class specifies all of the commonality of its derived classes.
> Cats and dogs have the common properties of all animals.
>
>> Claiming that formal systems make use of strings tells us absolutely
>> nothing which constrains the class of formal systems beyond what we
>> already know, so this contributes no useful information about what
>> counts as a formal system.
>
> You flat out ignored the rest of what I said.
> RELATIONS BETWEEN FINITE STRINGS.

But without specifying which relations are admissible and which are not
you, nor providing a way of evaluating the truth of those relations, you
are not providing any useful information.

> "cats are animals" "are" means <is a type of>
> "2 + 3 = 5" Equality relation
>
>
>>
>>>>> We can see that in any natural language system that the truth of any
>>>>> expression of conceptual knowledge only depends upon the meaning of
>>>>> the words of this expression.
>>>>
>>>> You might be able to see this. I, however, do not.
>>>
>>> Try to think of every (conceptual) declarative sentence that you have
>>> ever seen.
>>> Are there any of these sentences that can be verified as true by any
>>> other means
>>> than their meaning?
>>
>> 'Cats are mammals', which I believe you consider to be 'conceptual
>> knowledge' is verified by observation, not by the meanings of the words.
>>
>
> Two other people proved you wrong about this.

Two other people disagreed. They did not prove me wrong.

And how does one 'add' these two? compositionality refers specifically
to how meaning is built up using function composition which follows the
syntactic structure of a sentence. For example, the compositional
meaning of 'Jack gave Mary candy' would be established by

1) deriving a transitive verb 'gave Mary' whose semantics are determined
by the applying the function represented by the ditransitive verb 'gave'
to the argument 'Mary', i.e. gave(Mary).

2) deriving an intransitive verb 'gave Mary candy' whose semantics are
determined by the functional application (gave(Mary))(candy).

3) deriving a proposition 'Jack gave Mary candy' whose semantics are
determined by the functional application ((gave(Mary))(candy))(Jack).

This follows the syntactic structure of the sentence. Discourse context
is not part of the syntactic structure of the sentence.

> I could have linked to the Cyc project's Davidson representations but
> Cyc erased that fro their website. Once David Kleinecke saw that link
> the years long contention regarding compositionality was finally resolved.

What 'contention' was that?

> Here is the original paper by Davidson:
> http://semantics.uchicago.edu/kennedy/classes/s13/aspect/davidson67.pdf

I am familiar with Davidson's work. The paper you cite above has
absolutely nothing to do with discourse context. It concerns Davidson's
representation of event structure.

> it not not nearly as clear as the Cyc summary of it.

>
>>
>>>>> This same idea equally applies to formal systems. The truth of any
>>>>> expression of language only depends on the compositional meaning of
>>>>> this expression.
>>>>>
>>>>> **Conceptual knowledge:
>>>>> All knowledge that does not require any input from the sense organs
>>>>> to verify its truth.
>>>>
>>>> Which effectively rules out making claims about the world at all.
>>>> Truths which do not require any input from the sense organs
>>>> essentially limits you to talking about mathematics and logical
>>>> tautologies. Claims like 'cats are mammals' or 'cats are not
>>>> office-buildings' (two of your favourites) would be excluded.
>>>>
>>>> André
>>>>
>>>
>>> Not at all. "I saw Bill walk across the floor" would be excluded.
>>> "Bill walked across the floor" could be construed as a geometric
>>> "given".
>>
>> What is a 'geometric given'?
>
> A stipulated truth. It is taken to be true even if it is false.

What does 'geometric' have to do with this? And if 'Bill walked across
the floor' is stipulated to be true, how does that suddenly become
'conceptual knowledge' according to your definition?

André

>>
>> André
>>
>>> World knowledge is not ultimately excluded, it is only excluded for
>>> now to reduce the complexity of the analysis.
>>>
>>
>>
>
>


--

[peteolcott]

WHAT THE HELL ELSE COULD I MEAN BY ARCHITECTURE BLUE PRINTS FOR A BUILDING?

> And given you claim this architecture holds for all formal systems, I can assure you that 'inheritance hierarchies' cannot be part of it since most formal systems do not involve any concept of 'inheritance hierarchies'.
>

YOU SEEM TO BE AN IGNORAMUS AT LEAST AS THIS PERTAINS TO THE FUNDAMENTAL STRUCTURE OF KNOWLEDGE

>> A base class specifies all of the commonality of its derived classes.
>> Cats and dogs have the common properties of all animals.
>>
>>> Claiming that formal systems make use of strings tells us absolutely nothing which constrains the class of formal systems beyond what we already know, so this contributes no useful information about what counts as a formal system.
>>
>> You flat out ignored the rest of what I said.
>> RELATIONS BETWEEN FINITE STRINGS.
>
> But without specifying which relations are admissible and which are not you, nor providing a way of evaluating the truth of those relations, you are not providing any useful information.
>

DO YOU HAVE THE SLIGHTEST CLUE WHAT A RELATION IS?

Gödel 1944
Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote:

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

[temako...@gmail.com]

Can you, please, just address the issue of metaphor proving all your castles of pseudo-theoretical garbage wrong?

[André G. Isaak]

On 2019-09-11 5:46 p.m., peteolcott wrote:
> On 9/11/2019 12:13 PM, André G. Isaak wrote:
>> On 2019-09-11 9:54 a.m., peteolcott wrote:
>>> On 9/11/2019 3:33 AM, André G. Isaak wrote:
>>>> On 2019-09-10 11:37 p.m., peteolcott wrote:
>>>>> On 9/10/2019 11:56 PM, André G. Isaak wrote:
>>>>>> On 2019-09-10 9:50 p.m., peteolcott wrote:
>>>>>>> On 9/10/2019 10:16 PM, André G. Isaak wrote:
>>>>>>>> On 2019-09-10 9:23 a.m., peteolcott wrote:
>>>>>>>

<snippage>

>>>>> So you are unable to comprehend the concept of a common architecture
>>>>> across every formal system? Every formal system is specified using
>>>>> finite strings. Every formal system expresses relations between these
>>>>> finite strings. Since this seems so simple to me I can't see how this
>>>>> degree of specificity in unclear to you.
>>>>
>>>> But this 'common architecture' is entirely devoid of useful content.
>>>
>>> So you don't know anything about inheritance hierarchies?
>>
>> Where does your above claim mention 'inheritance hierarchies'? If this
>> was intended to be part of your 'common architecture', you would need
>> to have mentioned this in addition to 'finite strings' and 'relations
>> between finite strings'.
>>
>
> WHAT THE HELL ELSE COULD I MEAN BY ARCHITECTURE BLUE PRINTS FOR A BUILDING?

And how is this a meaningful response to what I wrote? You claimed there
was a common architecture across formal systems which you described as
follows: "Every formal system is specified using finite strings. Every

formal system expresses relations between these finite strings."

There is nothing in that description about inheritance hierarchies. So
what else is there in your common architecture which you have not
indicated in your description above?

>> And given you claim this architecture holds for all formal systems, I
>> can assure you that 'inheritance hierarchies' cannot be part of it
>> since most formal systems do not involve any concept of 'inheritance
>> hierarchies'.
>>
>
> YOU SEEM TO BE AN IGNORAMUS AT LEAST AS THIS PERTAINS TO THE FUNDAMENTAL
> STRUCTURE OF KNOWLEDGE

Q is a formal system; PA is a formal system; classical Propositional
Calculus is a formal system. Show me where any of these things make use
of an inheritance hierarchy. If you want to claim that this is part of
some 'common architecture' of all formal systems, then presumably all
formal systems would make use of this. They do not.

>>> A base class specifies all of the commonality of its derived classes.
>>> Cats and dogs have the common properties of all animals.
>>>
>>>> Claiming that formal systems make use of strings tells us absolutely
>>>> nothing which constrains the class of formal systems beyond what we
>>>> already know, so this contributes no useful information about what
>>>> counts as a formal system.
>>>
>>> You flat out ignored the rest of what I said.
>>> RELATIONS BETWEEN FINITE STRINGS.
>>
>> But without specifying which relations are admissible and which are
>> not you, nor providing a way of evaluating the truth of those
>> relations, you are not providing any useful information.
>>
>
> DO YOU HAVE THE SLIGHTEST CLUE WHAT A RELATION IS?

Yes, I do. But what does the quote below have to do with this? Gödel is
not offering a definition of 'relations' below. He is offering a
definition of 'types'.

> Gödel 1944
> Kurt Gödel in his 1944 Russell's mathematical logic gave the following
> definition of the "theory of simple types" in a footnote:
>
> By the theory of simple types I mean the doctrine which says that the
> objects of thought (or, in another interpretation, the symbolic
> expressions) are divided into types, namely: individuals, properties of
> individuals, relations between individuals, properties of such
> relations, etc. (with a similar hierarchy for extensions), and that
> sentences of the form: " a has the property φ ", " b bears the relation
> R to c ", etc. are meaningless, if a, b, c, R, φ are not of types
> fitting together.
>
>
>
>>> "cats are animals" "are" means <is a type of>

Just returning to this, putting <is a type of> in angle brackets assigns
a *name* to one of the relations which you claim exists, but it doesn't
define what this relation actually *means*. I can easily construe this
in a number of different ways, which have major consequences for
everything else in your alleged 'system'.

Are you construing 'animals' and 'cats' as sets of individuals where <is
a type of> asserts that cats are a subset of animals?

Or are you construing 'animals' as a set of sets, with 'cats' as an
element of that set?

Regardless, you clearly believe that there is more to your system than
simply 'finite strings' and 'relations'. You also assume a hierarchy
(which hasn't been defined), properties of your 'finite strings' which
can be inherited, sets (it would appear), and presumably much else, but
you have not actually defined any of this anywhere. Which leads me back
to my original claim, which is that your claim regarding a 'common
architecture' is an entirely empty claim until you actually spell out
what this 'common architecture' is *and* demonstrate that this is
actually present in all existing formal systems.

I ask again, what 'contention' are you referring to?

Again, please define your use of 'geometric'.

And since thus far the only relations which you have explicitly
mentioned with respect to you theory are 'equality' and 'is a type of',
please explain how 'Bill walked across the floor' can be represented
using only these two relations. Or are there other relations which your
system employs which you haven't yet mentioned? (Again, going back to my
claim that he haven't specified which relations your system makes use of).

André

[peteolcott]

On 9/11/2019 9:58 PM, André G. Isaak wrote:
> On 2019-09-11 5:46 p.m., peteolcott wrote:


>> Gödel 1944
>> Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote:
>>
By the theory of simple types I mean the doctrine which says
that the objects of thought (or, in another interpretation,
the symbolic expressions) are divided into types, namely:
individuals, properties of individuals, relations between
individuals, properties of such relations, etc. (with a
similar hierarchy for extensions), and that sentences of the
form: " a has the property φ ", " b bears the relation R to c
", etc. are meaningless, if a, b, c, R, φ are not of types fitting together.

Can you understand the above?

[André G. Isaak]

On 2019-09-11 9:53 p.m., peteolcott wrote:
> On 9/11/2019 9:58 PM, André G. Isaak wrote:
>> On 2019-09-11 5:46 p.m., peteolcott wrote:
>
>
> >> Gödel 1944
> >> Kurt Gödel in his 1944 Russell's mathematical logic gave the
> following definition of the "theory of simple types" in a footnote:
> >>
> By the theory of simple types I mean the doctrine which says
> that the objects of thought (or, in another interpretation,
> the symbolic expressions) are divided into types, namely:
> individuals, properties of individuals, relations between
> individuals, properties of such relations, etc. (with a
> similar hierarchy for extensions), and that sentences of the
> form: " a has the property φ ", " b bears the relation R to c
> ", etc. are meaningless, if a, b, c, R, φ are not of types fitting
> together.
>
> Can you understand the above?
>

Yes. And it has absolutely nothing to do with the points I made in my
post which you conveniently cut.

[peteolcott]

I am starting over because you lack the required prerequisite basis
for my other explanation.

Can you see how every element of the set of formal systems can be
specified on the basis of the above template?

[André G. Isaak]

No, because the above is simply false.

You've quoted an unnamed source quoting Gödel's summary of Russell's
type theory. Type theory is one aspect of some formal systems. It is
certainly not a 'template' describing 'every element of the set of
formal systems'. It plays no role at all, for example, in propositional
calculus, nor does it mention anything about relations between finite
strings nor inheritance hierarchies. And a formal theory consisting only
of a theory of types would be quite useless. You seem to be under the
misguided impression that because it contains the word 'relation' and
'hierarchy' that it has some relevance to the questions I asked. It does
not.

But, while on the topic of types, maybe you can clarify your <is a type
of> relation by answering the question I asked regarding the
relationship between cats and animals (the one you cut)

Do you consider 'animals' to be a set of individuals which includes cats
as a subset; or do you consider 'animals' to be a set of sets which
includes cats as an element?

[peteolcott]

ALL KNOWLEDGE ABOUT EVERYTHING IS IN AN INHERITANCE HIERARCHY

> And a formal theory consisting only of a theory of types would be quite useless. You seem to be under the misguided
> impression that because it contains the word 'relation' and 'hierarchy' that it has some relevance to the questions I asked. It does not.
>
> But, while on the topic of types, maybe you can clarify your <is a type of> relation by answering the question I asked regarding the relationship between cats and animals (the one you cut)
>
> Do you consider 'animals' to be a set of individuals which includes cats as a subset; or do you consider 'animals' to be a set of sets which includes cats as an element?
>
> André
>


--

[André G. Isaak]

So you claim, but the quote from Gödel you present says nothing
whatsoever about this. Nor have you ever offered a definition of an
'inheritance hierarchy'. I'm assuming your notion of an 'inheritance
hierarchy' is essentially that of C++, but that tells nothing about how
this is to be defined within a formal system which talks only of
relations between finite strings.

>

>> And a formal theory consisting only of a theory of types would be
>> quite useless. You seem to be under the misguided impression that
>> because it contains the word 'relation' and 'hierarchy' that it has
>> some relevance to the questions I asked. It does not.
>>
>> But, while on the topic of types, maybe you can clarify your <is a
>> type of> relation by answering the question I asked regarding the
>> relationship between cats and animals (the one you cut)
>>
>> Do you consider 'animals' to be a set of individuals which includes
>> cats as a subset; or do you consider 'animals' to be a set of sets
>> which includes cats as an element?

What exactly is your aversion to answering the above question? If you
don't like the options I presented, you're more than welcome to provide
a third alternative.

[peteolcott]

My aversion is that I really think that you are playing me and not actually interested in any honest dialogue.

[André G. Isaak]

That's an odd accusation considering you've changed topic with every
response in this thread thus far. The subthread started with your claim
that finite strings and relations between them accounted for all formal
systems. When I suggested that this was a largely vaccuous claim, you
responded by accusing me of not understanding inheritance hierarchies
(an entirely unrelated subject), and when asked about what relations you
allowed, you responded by given a definition of russell's type theory
(an entirely unrelated subject). When asked for clarification you
responded by repeating the definition of russell's type theory. So I now
am asking a question relevant to type theory (since apparently that's
what you're determined to talk about despite it not being part of your
original claim), and am then told I am not interested in actual dialogue.

The only conclusion I can reasonably draw is that you don't understand
any of these topics and are simply stringing them together because in
your mind they are all the same thing.

So for your edification: (1) The 'type hierarchies' referred to in
Gödel's definition have nothing to do with 'inheritance hierarchies',
and the discussion of relations in his definition describe constraints
which type theory imposes on which things relations can apply to but
says nothing whatsoever about which relations are defined within a
particular theory, which was my original question.

You really ought to try to understand people's posts before replying to
them. If you don't understand them, say so.

[peteolcott]

I still claim that, yet that is apparently over your head.
You don't seem to understand the formalist school much at
all and have a marked limitation lack of ability to see
the common properties of formal systems and generalize
them into higher level abstractions.

>When I suggested that this was a
> largely vaccuous claim, you responded by accusing me of not understanding inheritance hierarchies (an entirely unrelated subject),

The common properties of all formal systems can be collected
together in a base class such that all of the divergence of
the various formal systems can be specified in derived classes
from this base class.

This is the fundamental structure of the set of all conceptual
knowledge. The base class of animal collects together in one
place all of the common properties of all animals so that when
we talk about the derived class cats we simply inherit these
common properties from the base class.

> and when asked about what relations you allowed, you responded by given a definition of russell's type theory (an entirely
> unrelated subject).

https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944

sentences of the form: " a has the property φ ", "
b bears the relation R to c ", etc. are meaningless,
if a, b, c, R, φ are not of types fitting together.

Because I am ONLY talking about the base class and not talking
about the derived class your question was analogous to:
What do animals eat? Animals eat all kinds of different things
depending on the type of animals. Since I am only talking about
animals and not talking about cats, I have to respond with
an answer that applies to all animals. Animals eat food.

> When asked for clarification you responded by repeating the definition of russell's type theory. So I now am asking a question relevant to type theory (since apparently that's what you're determined to talk about despite it not being
> part of your original claim), and am then told I am not interested in actual dialogue.
>
> The only conclusion I can reasonably draw is that you don't understand any of these topics and are simply stringing them together because in your mind they are all the same thing.
>
> So for your edification: (1) The 'type hierarchies' referred to in Gödel's definition have nothing to do with 'inheritance hierarchies', and the discussion of relations in his definition describe constraints which type theory imposes on which things
> relations can apply to but says nothing whatsoever about which relations are defined within a particular theory, which was my original question.
>
> You really ought to try to understand people's posts before replying to them. If you don't understand them, say so.
>
> André
>
>


--

[peteolcott]

I have replaced my claim to the imperfectly defined term of the art:
analytic/synthetic distinction with my own definition of the term: [Conceptual knowledge]

Conceptual knowledge is every statement that can be verified as completely
true entirely based on its meaning without any input from the sense organs.
Copyright 2019 Pete Olcott

[peteolcott]

On 9/12/2019 6:39 AM, Fred wrote:

> On 12/09/2019 05:25, peteolcott wrote:
>> On 9/11/2019 11:08 PM, André G. Isaak wrote:
>>> On 2019-09-11 9:53 p.m., peteolcott wrote:
>>>> On 9/11/2019 9:58 PM, André G. Isaak wrote:
>>>>> On 2019-09-11 5:46 p.m., peteolcott wrote:
>>>>
>>>>
>>>>  >> Gödel 1944
>>>>  >> Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote:
>>>>  >>
>>>> By the theory of simple types I mean the doctrine which says
>>>> that the objects of thought (or, in another interpretation,
>>>> the symbolic expressions) are divided into types, namely:
>>>> individuals, properties of individuals, relations between
>>>> individuals, properties of such relations, etc. (with a
>>>> similar hierarchy for extensions), and that sentences of the
>>>> form: " a has the property φ ", " b bears the relation R to c
>>>> ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together.
>>>>
>>>> Can you understand the above?
>>>>
>>>
>>> Yes. And it has absolutely nothing to do with the points I made in my post which you conveniently cut.
>>>
>>> André
>>>
>>
>> I am starting over because you lack the required prerequisite basis
>> for my other explanation.
>>
>> Can you see how every element of the set of formal systems can be
>> specified on the basis of the above template?
>

> The above template being Gödel's footnote?  What do mean by an element of a formal system.
>

Here is the question that I am answering:
When construed within the mathematical formalist school what common
properties would every element of the set of formal systems have.

[André G. Isaak]

So you've changed the subject altogether once again. You are no longer
considering your system in which all conceptual knowledge can be
represented as strings and relations between strings. Instead you are
trying to visualize the entire set of formal systems (of which you are
familiar with only a tiny fraction) as if they were some giant C++
program? To what end?

> This is the fundamental structure of the set of all conceptual
> knowledge. The base class of animal collects together in one
> place all of the common properties of all animals so that when
> we talk about the derived class cats we simply inherit these
> common properties from the base class.
>
>> and when asked about what relations you allowed, you responded by
>> given a definition of russell's type theory (an entirely unrelated
>> subject).
>
> https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
> sentences of the form: " a has the property φ ", "
> b bears the relation R to c ", etc. are meaningless,
> if a, b, c, R, φ are not of types fitting together.
>
> Because I am ONLY talking about the base class and not talking
> about the derived class your question was analogous to:
> What do animals eat? Animals eat all kinds of different things
> depending on the type of animals. Since I am only talking about
> animals and not talking about cats, I have to respond with
> an answer that applies to all animals. Animals eat food.

So what does Russell's type theory have to do with this at all? The set
of formal systems certainly doesn't share Russell's type theory. Many
don't have a type theory at all.

What I was asking about was *your* system, the one in which all
conceptual knowledge is encoded as relations between finite strings, not
about some 'metatheory of formal theories'. And I am still interested in
that question regarding your <is a type of> relation.

To rephrase my question in a different way, I was asking about your
claim that 'cats' <is a type of> 'animals'. Do you consider 'cats' and
'animals' to be of the same type or of different types? What is the type
of 'cat(s)' and the type of 'animal(s)'?

>
>>  When asked for clarification you responded by repeating the
>> definition of russell's type theory. So I now am asking a question
>> relevant to type theory (since apparently that's what you're
>> determined to talk about despite it not being part of your original
>> claim), and am then told I am not interested in actual dialogue.
>>
>> The only conclusion I can reasonably draw is that you don't understand
>> any of these topics and are simply stringing them together because in
>> your mind they are all the same thing.
>>
>> So for your edification: (1) The 'type hierarchies' referred to in
>> Gödel's definition have nothing to do with 'inheritance hierarchies',
>> and the discussion of relations in his definition describe constraints
>> which type theory imposes on which things relations can apply to but
>> says nothing whatsoever about which relations are defined within a
>> particular theory, which was my original question.
>>
>> You really ought to try to understand people's posts before replying
>> to them. If you don't understand them, say so.
>>
>> André
>>
>>
>
>


--

[André G. Isaak]

Which still faces the same issue. Neither 'cats are mammals' nor 'cats
are not buildings' would count as conceptual knowledge by that
definition. Very few things would count as conceptual knowledge
(basically just math).

[Jeff Barnett]

André G. Isaak wrote on 9/12/2019 10:12 AM:
> On 2019-09-12 9:31 a.m., peteolcott wrote:

<CRAP CUT>

> So what does Russell's type theory have to do with this at all? The set
> of formal systems certainly doesn't share Russell's type theory. Many
> don't have a type theory at all.
>
> What I was asking about was *your* system, the one in which all
> conceptual knowledge is encoded as relations between finite strings, not
> about some 'metatheory of formal theories'. And I am still interested in
> that question regarding your <is a type of> relation.
>
> To rephrase my question in a different way, I was asking about your
> claim that 'cats' <is a type of> 'animals'. Do you consider 'cats' and
> 'animals' to be of the same type or of different types? What is the type
> of 'cat(s)' and the type of 'animal(s)'?

If you look at my recent thread "Comments on ..." you will notice that
Dumb F...k's inference rule of choice cannot, I repeat CANNOT do subtype
or in fact any type-related inferences let alone property inheritance.
In one thread he has taken an atomic bomb to 15 years of useless
thought. He surely has proven to be a knucklehead beyond repair as well
as beyond the limited understanding of mortals. My guess is he hasn't
paused for 15 minutes to think in those 15 years; and it's now shown in
his full circle contradictions. The toxic fumes are everywhere he tries
to contribute,
--
Jeff Barnett

[peteolcott]

Specified relations between finite strings would seem to have the same expressive power as lambda calculus.

[Jeff Barnett]

Your rule of inference WILL NOT ALLOW any deductions. Your calculus is
as dead as your brain.
--
Jeff Barnett

[peteolcott]

My whole notion of a formal system is specified relations between finite strings.

If we specify these relations: "8 > 5", "5 > 3" then we have this deduction:

"8 > 5"
"5 > 3"
-------
"8 > 3"

[Jeff Barnett]

You are absurd: In a thread recently started by YOU, you define your
inference operator as "and"!!!!!!!! Remember o crap for brains??? Now
even you might (but maybe not) be able to work out that "and" can't do
your example above nor can it do transitive relations such as subset.
You have made many, many, many stupid mistakes and showed pride in your
status as an ignoramus but this time you have cut of all paths out of
the nonsense. Maybe you would like to reintroduce your TM that does
halting to try to change the topic and avoid the humiliation you have so
richly earned but it wouldn't work this time either. Rather than trying
another nonsensical non sequitur answer which makes you look dumber than
ever, just put me in your kill file; that's a task that a moderate
junior coder like you just might get right.
--
Jeff Barnett

[peteolcott]

On 9/12/2019 6:01 PM, Jeff Barnett wrote:
> peteolcott wrote on 9/12/2019 3:50 PM:
>> On 9/12/2019 4:28 PM, Jeff Barnett wrote:
>>> peteolcott wrote on 9/12/2019 3:25 PM:
>>>> On 9/12/2019 3:43 PM, Jeff Barnett wrote:
>>>>> André G. Isaak wrote on 9/12/2019 10:12 AM:
>>>>>> On 2019-09-12 9:31 a.m., peteolcott wrote:
>>>>>        <CRAP CUT>
>>>>>> So what does Russell's type theory have to do with this at all? The set of formal systems certainly doesn't share Russell's type theory. Many don't have a type theory at all.
>>>>>>
>>>>>> What I was asking about was *your* system, the one in which all conceptual knowledge is encoded as relations between finite strings, not about some 'metatheory of formal theories'. And I am still interested in that question regarding your <is a type
>>>>>> of> relation.
>>>>>>
>>>>>> To rephrase my question in a different way, I was asking about your claim that 'cats' <is a type of> 'animals'. Do you consider 'cats' and 'animals' to be of the same type or of different types? What is the type of 'cat(s)' and the type of 'animal(s)'?
>>>>>
>>>>> If you look at my recent thread "Comments on ..." you will notice that Dumb F...k's inference rule of choice cannot, I repeat CANNOT do subtype or in fact any type-related inferences let alone property inheritance. In one thread he has taken an atomic
>>>>> bomb to 15 years of useless thought. He surely has proven to be a knucklehead beyond repair as well as beyond the limited understanding of mortals. My guess is he hasn't paused for 15 minutes to think in those 15 years; and it's now shown in his full
>>>>> circle contradictions. The toxic fumes are everywhere he tries to contribute,
>>>>
>>>> Specified relations between finite strings would seem to have the same expressive power as lambda calculus.
>>>
>>> Your rule of inference WILL NOT ALLOW any deductions. Your calculus is as dead as your brain.
>>
>> My whole notion of a formal system is specified relations between finite strings.
>>
>> If we specify these relations: "8 > 5", "5 > 3" then we have this deduction:
>>
>> "8 > 5"
>> "5 > 3"
>> -------
>> "8 > 3"
>
> You are absurd: In a thread recently started by YOU,

I just proved my point that deduction from specified relations between
finite strings works properly thus directly refuting your point.
YOUR DISHONESTY ABOUT THIS IS OBVIOUS TO ALL !!!
YOUR DISHONESTY ABOUT THIS IS OBVIOUS TO ALL !!!
YOUR DISHONESTY ABOUT THIS IS OBVIOUS TO ALL !!!
YOUR DISHONESTY ABOUT THIS IS OBVIOUS TO ALL !!!
YOUR DISHONESTY ABOUT THIS IS OBVIOUS TO ALL !!!
YOUR DISHONESTY ABOUT THIS IS OBVIOUS TO ALL !!!

> you define your inference operator as "and"!!!!!!!! Remember o crap for brains??? Now even you might (but maybe not) be able to work out that "and" can't do your example above nor can it do transitive
> relations such as subset. You have made many, many, many stupid mistakes and showed pride in your status as an ignoramus but this time you have cut of all paths out of the nonsense. Maybe you would like to reintroduce your TM that does halting to try to
> change the topic and avoid the humiliation you have so richly earned but it wouldn't work this time either. Rather than trying another nonsensical non sequitur answer which makes you look dumber than ever, just put me in your kill file; that's a task that
> a moderate junior coder like you just might get right.


--

[André G. Isaak]

On 2019-09-12 10:12 a.m., André G. Isaak wrote:

> To rephrase my question in a different way, I was asking about your
> claim that 'cats' <is a type of> 'animals'. Do you consider 'cats' and
> 'animals' to be of the same type or of different types? What is the type
> of 'cat(s)' and the type of 'animal(s)'?

Still awaiting an answer to the above.

[peteolcott]

On 9/12/2019 6:35 PM, Fred wrote:

> On 12/09/2019 22:25, peteolcott wrote:
>
>> Specified relations between finite strings would seem to have the same expressive power as lambda calculus.
>

> Well, let's find out shall we?  We begin by looking up lambda calculus, maybe in Wikipedia, and reading about it.  If we wish to know more there are plenty of links and references.  After some study we form a good idea of what lambda calculus is and what
> its expressive power is (but see footnote).  Now we turn to Pete's specified relations between finite strings hoping to proceed in a similar way.  But where can we find out what it is?  We ask Pete, but all he ever does is repeat "specified relations
> between finite strings" and we get no where.
>
> Footnote: if it's expressive power you want, stick to plain English.
>
>

Lambda Calculus IS ALREADY SPECIFIED RELATIONS BETWEEN FINITE STRINGS
with the expressive power of a Turing Machine, thus able to express
any formal system.

[Jeff Barnett]

I think you should specialize in tantrums as the above. There's no
dishonesty here save your nonsense. Surely you haven't forgotten your
new inference rule and proof operator with a truth table? Of AND no
less! If you would get your hand out of your pants and concentrate
before replying. you just might appear more mature. Your mistakes are
obvious to every one reading these threads as is your infantile style of
tantrum.

[peteolcott]

I don't waste my time tediously defining things that are already completely defined.

> Of AND no less! If you would get your hand out of your pants
> and concentrate before replying. you just might appear more mature. Your mistakes are obvious to every one reading these threads as is your infantile style of tantrum.
>
>>>  you define your inference operator as "and"!!!!!!!! Remember o crap for brains??? Now even you might (but maybe not) be able to work out that "and" can't do your example above nor can it do transitive relations such as subset. You have made many, many,
>>> many stupid mistakes and showed pride in your status as an ignoramus but this time you have cut of all paths out of the nonsense. Maybe you would like to reintroduce your TM that does halting to try to change the topic and avoid the humiliation you have
>>> so richly earned but it wouldn't work this time either. Rather than trying another nonsensical non sequitur answer which makes you look dumber than ever, just put me in your kill file; that's a task that a moderate junior coder like you just might get
>>> right.
>>
>>
>