Eliminating undecidability in formal systems

[PeteOlcott]

When the formal notion of truth is defined in this way, all
previously undecidable logic sentences become decidable:

When Closed WFF x of formal system F is considered:
True----------its a theorem of F: ---------------(F ⊢ x)
False----------its negation is a theorem of F: (F ⊢ ¬x)
¬True---------its not a theorem of F: ----------(F ⊬ x)
¬Boolean-----its neither True nor False in F: (F⊬x ∧ F⊬¬x)

When-so-ever any closed WFF contains a ¬Boolean term the whole
WFF evaluates to ¬True thus maintaining consistency within the
{axioms of truth} adaptation to the notion of a formal system.

Eliminating Undecidability and Incompleteness in Formal Systems
https://www.researchgate.net/publicatio ... al_Systems

The above adaptations show how this logic sentence is ¬Boolean thus ¬True:
∃F ∈ Formal_Systems ∃G ∈ WFF(F) (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G)))

Making the following paragraph ¬Boolean, thus ¬True
The first incompleteness theorem states that in any consistent formal system F
within which a certain amount of arithmetic can be carried out, there are
statements of the language of F which can neither be proved nor disproved in F.
(Raatikainen 2018)

[Logik]

There is no "sufficiency" criterion in your definition.

[PeteOlcott]

There is no "sufficiency" criterion in your definition.

I have no idea what you mean.
Necessary truths logically entail other necessary truths.

[Logik]

There is no "sufficiency" criterion in your definition.

I have no idea what you mean.
Necessary truths logically entail other necessary truths.

A set of facts "adds up" to be true.

So if the set was one element short, would it still "add up" ?

[PeteOlcott]

There is no "sufficiency" criterion in your definition.

I have no idea what you mean.
Necessary truths logically entail other necessary truths.

A set of facts "adds up" to be true.

So if the set was one element short, would it still "add up" ?

(1) It is raining outside.
(2) I go outside unprotected from the rain.
∴ I get wet.
Eliminate "fact" (2) and see what happens.

[Logik]

I have no idea what you mean.
Necessary truths logically entail other necessary truths.

A set of facts "adds up" to be true.

So if the set was one element short, would it still "add up" ?

(1) It is raining outside.
(2) I go outside unprotected from the rain.
∴ I get wet.
Eliminate "fact" (2) and see what happens.

The same thing as if I were to jump into the swimming pool.
The same thing if you were to pour a bucket of water over my head.
The same thing that happens when I take a shower every morning.

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

What's your point?

[PeteOlcott]

A set of facts "adds up" to be true.

So if the set was one element short, would it still "add up" ?

(1) It is raining outside.
(2) I go outside unprotected from the rain.
∴ I get wet.
Eliminate "fact" (2) and see what happens.

The same thing as if I were to jump into the swimming pool.
The same thing if you were to pour a bucket of water over my head.
The same thing that happens when I take a shower every morning.

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

What's your point?

When I directly answer your question YOU DON'T EVEN NOTICE ???
If the set is one element short then IT NO LONGER ADDS UP!

A set of facts "adds up" to be true.

So if the set was one element short, would it still "add up" ?

[Logik]

When I directly answer your question YOU DON'T EVEN NOTICE ???
If the set is one element short then IT NO LONGER ADDS UP!

Seriously. I am pointing out to you that it DOES ADD UP.
In a DIFFERENT WAY. It is called Equifinality.

Allow me to refer you back too my FIRST COMMENT

There is no "sufficiency" criterion in your definition.

What does it mean for things to "add up"? Add up to what ?!?

[PeteOlcott]

When I directly answer your question YOU DON'T EVEN NOTICE ???
If the set is one element short then IT NO LONGER ADDS UP!

Seriously. I am pointing out to you that it DOES ADD UP.
In a DIFFERENT WAY. It is called Equifinality.

Allow me to refer you back too my FIRST COMMENT

There is no "sufficiency" criterion in your definition.

What does it mean for things to "add up"? Add up to what ?!?

So in other words you are concluding that when-so-ever it is raining
outside you would always get wet even if you stay inside.

That sounds very screwy to me. I have very much experience with
responding to deceptive dodges. If you so not directly address the
above point a deceptive dodge will be my (perhaps final) conclusion
on the value of talking to you.

[Logik]

So in other words you are concluding that when-so-ever it is raining
outside you would always get wet even if you stay inside.

No! I am saying the exact opposite!

There are very many ways to get wet none of which require rain.

That sounds very screwy to me. I have very much experience with
responding to deceptive dodges. If you so not directly address the
above point a deceptive dodge will be my (perhaps final) conclusion
on the value of talking to you.

Ironic. Your threat to abort the conversation is a dodge.

I asked you to define your criterion for "sufficienty" (what does "add up" mean?)
I pointed you to the concept of Equifinality.

You said: "A set of facts adds up to X being TRUE."
(1) It is raining outside.
(2) I go outside unprotected from the rain.
∴ I get wet.

I heard:
f(x) = Wet()

[PeteOlcott]

So in other words you are concluding that when-so-ever it is raining
outside you would always get wet even if you stay inside.

No! I am saying the exact opposite!

There are very many ways to get wet none of which require rain.

That sounds very screwy to me. I have very much experience with
responding to deceptive dodges. If you so not directly address the
above point a deceptive dodge will be my (perhaps final) conclusion
on the value of talking to you.

Ironic. Your threat to abort the conversation is a dodge.

I asked you to define your criterion for "sufficienty" (what does "add up" mean?)
I pointed you to the concept of Equifinality.


f(x) = wet !

OK that was a reasonable response.
There is no set of facts that add up to X being TRUE.

Where a fact is:
(1) A true premise of sound deductive inference or
(2) A Haskell Curry {elementary statement} more conventionally called an axiom

and TRUE is:
(1) The conclusion of sound deductive inference or
(2) A Haskell Curry {epistatement} more conventionally called a theorem

I have to refer to the Haskell Curry notion of formal system because
many definitions of the term "axiom" is something that is true-ish
rather than exactly true.

http://liarparadox.org/Haskell_Curry_45.pdf

[PeteOlcott]

So in other words you are concluding that when-so-ever it is raining
outside you would always get wet even if you stay inside.

No! I am saying the exact opposite!

There are very many ways to get wet none of which require rain.

That sounds very screwy to me. I have very much experience with
responding to deceptive dodges. If you so not directly address the
above point a deceptive dodge will be my (perhaps final) conclusion
on the value of talking to you.

Ironic. Your threat to abort the conversation is a dodge.

I asked you to define your criterion for "sufficienty" (what does "add up" mean?)
I pointed you to the concept of Equifinality.

You said: "A set of facts adds up to X being TRUE."
(1) It is raining outside.
(2) I go outside unprotected from the rain.
∴ I get wet.

I heard:
f(x) = Wet()

So basically you don't hear my answer because you make sure to ignore key details.
I provided a concrete example of sound deductive inference.

When the conclusion logically follows from the set of true premises it adds up to true
conversely when the conclusion does not logically follow from the set of true premises
it fails to add up to true. Its not really that hard.

[Logik]

So basically you don't hear my answer because you make sure to ignore key details.
I provided a concrete example of sound deductive inference.

Yeah, but I thought you had some ground-breaking discovery when you are demonstrating logic 101 stuff. That's an awful lot of time to study logic to come to this level of understanding. Most of the software engineering interns I hire are far beyond this level of understanding.

And besides - it has temporal edge cases.

(1) It is raining outside.
(2) I go outside unprotected from the rain.
(3) I didn't get wet, because it stopped raining by the time I got outside

When the conclusion logically follows from the set of true premises it adds up to true
conversely when the conclusion does not logically follow from the set of true premises
it fails to add up to true. Its not really that hard.

Q.E.D Yes. We all know what the definition of deduction is.

The error you are making is that you believe you can actually employ deductive reasoning in a temporal universe. You can't. Because you are very very short on universally true axioms.

Because. even IF we accept your argument to be valid and sound, experience is always the final arbiter.
If it's raining outside, and I go outside unprotected and I DON'T get wet (for whatever reason)

That's called? Falsification.

How would that possibly happen in practice? Simple. Ever seen it rain only on one side of the street? It was raining - I didn't get wet.

[PeteOlcott]

So basically you don't hear my answer because you make sure to ignore key details.
I provided a concrete example of sound deductive inference.

Yeah, but I thought you had some ground-breaking discovery when you are demonstrating logic 101 stuff. That's an awful lot of time to study logic to come to this level of understanding. Most of the software engineering interns I hire are far beyond this level of understanding.

The groundbreaking discovery is that I derived a very slight change to the way that formal
systems are defined such that incompleteness is impossible in any of these formal systems.

The only reason that the Tarski proof seemed to succeed is because Tarski was assuming
an incorrect formalization of the notion of truth that failed to detect semantically incorrect
expressions of language. True and False are the atoms of semantics.

[Logik]

True and False are the atoms of semantics.

No, they are the atoms of black-and-white thinking.

Probabilities, modal and quantum logics are the atoms of plausible reasoning.

Which is what most of us employ day-to-day in this universe.