Simply defining Gödel Incompleteness away

[Skepdick]

My end goal is to make a very easy way to formalize every subtle nuance of natural
language semantics.

You can't formalize semantics. All you can ever formalize is grammar.

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

[PeteOlcott]

The above definition allows the principle of explosion. This must be forbidden.

You are really not hearing me!

The principle of explosion is what I WANT in my systems.

I prefer proving too much (everything even!) than proving too little.

It does not really matter what you want. Proving too much compared to proving
exactly the right amount is the difference of incorrect versus correct.

[PeteOlcott]

My end goal is to make a very easy way to formalize every subtle nuance of natural
language semantics.

You can't formalize semantics. All you can ever formalize is grammar.

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

Montague grammar is the grammar of semantics.

[Skepdick]

It does not really matter what you want. Proving too much compared to proving
exactly the right amount is the difference of incorrect versus correct.

You still don't fucking understand Godel!

You can't prove "exactly the right amount". There are such things as true-but-unprovable statements!

tumblr_mc81o59oEh1rugavko1_1280.jpg (58.5 KiB) Viewed 2571 times

[Skepdick]

Montague grammar is the grammar of semantics.

Yes. The GRAMMAR of the semantics. Not the semantics of the semantics.

That's why they are called FORMALISMS. Because FORM.

[PeteOlcott]

It does not really matter what you want. Proving too much compared to proving
exactly the right amount is the difference of incorrect versus correct.

You still don't fucking understand Godel!

You can't prove "exactly the right amount". There are such things as true-but-unprovable statements!
tumblr_mc81o59oEh1rugavko1_1280.jpg

I just proved that there is no such thing as true-but-unprovable statements
in this message: Mon Jun 15, 2020 4:23 pm

Its as easy as: 1,2,3...
(1) If sound deductive inference does not reach its conclusion then its conclusion is not derived.
(2) Its conclusion only counts as true after it have been derived.
(3) Sound deductive inference is the ONLY correct model of analytical truth.

[Skepdick]

I just proved that there is no such thing as true-but-unprovable statements

You just proved that your own system is consistent?

THEN YOUR SYSTEM IS INCONSISTENT!!!

How many fucking times do you need this explained?

This statement is true and unprovable.

[PeteOlcott]

I just proved that there is no such thing as true-but-unprovable statements

You just proved that your own system is consistent?

THEN YOUR SYSTEM IS INCONSISTENT!!!

How many fucking times do you need this explained?

This statement is true and unprovable.

Self-contradictory statements are rejected as incorrect.
"This sentence is not true" is indeed {not true} yet that does not make it
true because it has the self-contradiction error.

[Skepdick]

Self-contradictory statements are rejected as incorrect.
"This sentence is not true" is indeed {not true} yet that does not make it
true because it has the self-contradiction error.

Yeah, but the sentence "This statement is unprovable." is true! There is no contradiction.

The contradiction only arrises because YOU have defined "truth" and "provability" as the same thing when they are not!

So if your system can prove the above statement it renders itself inconsistent! That's a good thing!!! Consistent systems suck because they are incomplete.

Fuck consistency. Get rid of it!

[PeteOlcott]

Self-contradictory statements are rejected as incorrect.
"This sentence is not true" is indeed {not true} yet that does not make it
true because it has the self-contradiction error.

Yeah, but the sentence "This statement is unprovable." is true! There is no contradiction.

The contradiction only arrises because YOU have defined "truth" and "provability" as the same thing when they are not!

So if your system can prove the above statement it renders itself inconsistent! That's a good thing!!! Consistent systems suck because they are incomplete.

"This sentence is not provable" cannot possibly be true because:

If we decide that the sentence is true on the basis of the diagonal argument
then this diagonal argument basis forms a proof thus making the sentence
self-contradictory. By what-so-ever means that we do decide that the sentence
is true is a formal proof of its truth making the sentence self contradictory.

It is self-evident that self-contradictory sentences are incorrect.


Copyright 2020 Pete Olcott

[Skepdick]

"This sentence is not provable" cannot possibly be true because.

It is true! What makes it true is the fact that you can't prove it.

If we decide that the sentence is true on the basis of the diagonal argument
then this diagonal argument basis forms a proof thus making the sentence
self-contradictory. By what-so-ever means that we do decide that the sentence
is true is a formal proof of its truth making the sentence self contradictory.

I am deciding that it's true on the basis that I fucking say it is! I am saying it informally - I don't need a formal system to prove to me that what I am saying is true.

If you need a formal system - go ahead and prove the unprovable sentence.

It is self-evident that self-contradictory sentences are incorrect.

It's self-evident to me that self-contradictory sentences are correct!

It's just language, damn it! Its purpose is expression and communication. Why are you trying to limit expression with your fucking rules?

[PeteOlcott]

"This sentence is not provable" cannot possibly be true because.

It is true! What makes it true is the fact that you can't prove it.

If we decide that the sentence is true on the basis of the diagonal argument
then this diagonal argument basis forms a proof thus making the sentence
self-contradictory. By what-so-ever means that we do decide that the sentence
is true is a formal proof of its truth making the sentence self contradictory.

I am deciding that it's true on the basis that I fucking say it is! I am saying it informally - I don't need a formal system to prove to me that what I am saying is true.

If you need a formal system - go ahead and prove the unprovable sentence.

It is self-evident that self-contradictory sentences are incorrect.

It's self-evident to me that self-contradictory sentences are correct!

It's just language, damn it! Its purpose is expression and communication. Why are you trying to limit expression with your fucking rules?

Like I said if there is any actual basis that it is true then what-so-ever that actual basis
is would be a proof that makes it self-contradictory otherwise there is no actual basis
what-so-ever to show that it is true. There is no way out of this. If it is unprovable
then it is untrue. If it is true then it is provable.

[Skepdick]

If it is true then it is provable.

OK. So is the above "true"? Prove it.

If you can't prove it then it's untrue, right?

[Eodnhoj7]

I just proved that there is no such thing as true-but-unprovable statements

You just proved that your own system is consistent?

THEN YOUR SYSTEM IS INCONSISTENT!!!

How many fucking times do you need this explained?

This statement is true and unprovable.

Self-contradictory statements are rejected as incorrect.
"This sentence is not true" is indeed {not true} yet that does not make it
true because it has the self-contradiction error.

There is no statement that is not self contradictory given that each statement is a localization of a continuum thus representing a part of the whole. As representative of a part, each statement always requires some statement, unrepresented, beyond it. It is this absence of a complete representation that necessitates a contradiction in terms given that something is always provable by what is not provable. With the increase in words comes an increase in contradictions. However with the increase in words, as an increase in contradictions, comes a necessary further increase in words to clarify the contradictions.

[PeteOlcott]

If it is true then it is provable.

OK. So is the above "true"? Prove it.

If you can't prove it then it's untrue, right?

∀F ∈ Formal_System
∀X ∈ Language(F)
(((F ⊬ X) ∧ (F ⊬ ¬X)) ↔ Undecidable(F, X))

Gödel says that Undecidable(F, X) means Incomplete(F).

From the sound deductive inference model we can see that this is incorrect. A sound deduction begins with premises that are known to be true and applies truth preserving operations to these premises deriving a conclusion known to be true.

If there is an unprovability break between the premises and conclusion then the conclusion is not derived and the argument is invalid.

If there is an unprovability break between the premises and negation of the conclusion then the negation of the conclusion is not derived and the argument is invalid.

Within the sound deductive inference model Undecidable(F, X)) simply means Invalid(F,X) and when Gödel says that is means Incomplete(F) he is simply wrong.

Copyright 2020 Pete Olcott