What the theorems of Incompleteness or Undecidability assert...

What is the basis for reason? And mathematics?

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Logik
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by Logik » Wed Feb 27, 2019 1:26 am

Scott Mayers wrote:
Wed Feb 27, 2019 1:10 am
I have to say I like your background even if we might not be precisely in agreement.

This actually proves something about reality itself and similar to what I used to demonstrate HOW you can begin with absolutely nothing in totality to derive something. That is, you think that the computer program is presenting a contradiction when it is actually the underlying logic of reality itself (as a whole).
information :) It's everywhere. 1s and 0s. Trues and Falses.
Scott Mayers wrote:
Wed Feb 27, 2019 1:10 am
1,0

0 == (0 and 1)

but

1 != (0 and 1)

...which implies that 1 can only equal itself.... an Identity.
I can't decide if Aristotle made an error of if he was a genius.

Scott Mayers wrote:
Wed Feb 27, 2019 1:10 am
Assigning 0 to (A == A) is equivalent to assigning 0 == 1 in a way that one might say, "From nothing, we can get something."
See! Inversion! :)

Eventually you start questioning those damn "laws" and you begin to contradict THEM out of our own mind.
And you emerge on the other side with intuitionistic logic.

The laws are like training wheels until you can learn to think :)
And then you can take off the training wheels yourself.

I am going to finish responding to the rest of your post in the morning. It's 2am. My brain scanned over it and said "cannot compute".
Last edited by Logik on Wed Feb 27, 2019 1:27 am, edited 1 time in total.

surreptitious57
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 1:27 am

Logic wrote:
You cannot prove ANYTHING about reality with logic . NOTHING . NADA . ZILCH . ZIP
The concept of proof is valid only within the context of logic NOT in the context of using logic FOR THE PURPOSES OF reasoning about reality
Logic is fundamentally the systematic study of argument form and inference and paradox / contradiction
It is an attempt to make sense of assumptions about the world that are not based upon direct observation
By contrast reason is the application of logic with reference to understanding the world as it appears to be
Reason is therefore a sub set of logic within the hierarchy of epistemology

Proof is not only valid within the context of logic but also empiricism
For example Einsteins Theory Of General Relativity disproved / falsified Newtons Theory Of Universal Gravitation
This was demonstrated by the orbit of Mercury which had a 43 arc second discrepancy that only GR could explain

Disproof / falsification of a hypothesis is the best way to obtain knowledge about the observable world
Knowledge that would be unreliable if it could not be empirically demonstrated since it could be false

The word science is derived from the Latin root scientia which literally means knowledge / to know
You cannot know anything about natural phenomena just by assuming it since that is not knowledge

Logik
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by Logik » Wed Feb 27, 2019 1:28 am

surreptitious57 wrote:
Wed Feb 27, 2019 1:27 am
Logic wrote:
You cannot prove ANYTHING about reality with logic . NOTHING . NADA . ZILCH . ZIP
The concept of proof is valid only within the context of logic NOT in the context of using logic FOR THE PURPOSES OF reasoning about reality
Logic is fundamentally the systematic study of argument form and inference and paradox / contradiction
It is an attempt to make sense of assumptions about the world that are not based upon direct observation
By contrast reason is the application of logic with reference to understanding the world as it appears to be
Reason is therefore a sub set of logic within the hierarchy of epistemology

Proof is not only valid within the context of logic but also empiricism
For example Einsteins Theory Of General Relativity disproved / falsified Newtons Theory Of Universal Gravitation
This was demonstrated by the orbit of Mercury which had a 43 arc second discrepancy that only GR could explain

Disproof / falsification of a hypothesis is the best way to obtain knowledge about the observable world
Knowledge that would be unreliable if it could not be empirically demonstrated since it could be false

The word science is derived from the Latin root scientia which literally means knowledge / to know
You cannot know anything about natural phenomena just by assuming it since that is not knowledge
Logic is the study of abstract structure/patterns. Logic is metaphysics. Logic/Mathematics/Computer science/Physics are all merged into one.

As of a few days ago I am 100% convinced that Lambda calculus is the ultimate metaphysic ( https://en.wikipedia.org/wiki/Metalanguage )

Once you have acquired knowledge you express it in language/logic/mathematics

surreptitious57
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 2:08 am

Logic wrote:
Logic / Mathematics / Computer science / Physics are all merged into one
Logic is the foundation of both philosophy and mathematics but they are also separate disciplines
Computer science is a branch of both mathematics and science which are also separate disciplines

Disciplines are also separated by time : physics came first [ Big Bang ] then chemistry then biology

Also logic like science is not a simple discipline but many variations within the general definition :
Classical / Temporal / Fuzzy / Modal / Categorical / Constructive / Ordinal / Doxastic / Infinitary

surreptitious57
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Joined: Fri Oct 25, 2013 6:09 am

Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 2:23 am

Logic wrote:
Once you have acquired knowledge you express it in language / logic / mathematics
Yes you can but you still need a reliable methodology that can demonstrate that what you actually have is knowledge
If your observations about the world are not rigorous enough then language / logic / mathematics will also be no use

This is why from a scientific perspective empiricism is the most important thing of all
The map is very important but not as much as the thing being studied : the territory

Scott Mayers
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Location: Saskatoon, SK, Canada

Re: What the theorems of Incompleteness or Undecidability assert...

Post by Scott Mayers » Wed Feb 27, 2019 2:27 am

surreptitious57 wrote:
Wed Feb 27, 2019 2:08 am
Logic wrote:
Logic / Mathematics / Computer science / Physics are all merged into one
Logic is the foundation of both philosophy and mathematics but they are also separate disciplines
Computer science is a branch of both mathematics and science which are also separate disciplines

Disciplines are also separated by time : physics came first [ Big Bang ] then chemistry then biology

Also logic like science is not a simple discipline but many variations within the general definition :
Classical / Temporal / Fuzzy / Modal / Categorical / Constructive / Ordinal / Doxastic / Infinitary
Welcome to the discussion surreptitious57. I gather that logik shares much the same views but we all come from distinct approaches. Does your own background reach the classics of Plato and Aristotle?

And do you also agree to the motivational problems from the first post? (or agree to these as what you might have asked yourself on these independent of reading by other philosophers?

Scott Mayers
Posts: 1391
Joined: Wed Jul 08, 2015 1:53 am
Location: Saskatoon, SK, Canada

Re: What the theorems of Incompleteness or Undecidability assert...

Post by Scott Mayers » Wed Feb 27, 2019 2:39 am

Logik wrote:
Wed Feb 27, 2019 1:26 am
Scott Mayers wrote:
Wed Feb 27, 2019 1:10 am
I have to say I like your background even if we might not be precisely in agreement.

This actually proves something about reality itself and similar to what I used to demonstrate HOW you can begin with absolutely nothing in totality to derive something. That is, you think that the computer program is presenting a contradiction when it is actually the underlying logic of reality itself (as a whole).
information :) It's everywhere. 1s and 0s. Trues and Falses.
Scott Mayers wrote:
Wed Feb 27, 2019 1:10 am
1,0

0 == (0 and 1)

but

1 != (0 and 1)

...which implies that 1 can only equal itself.... an Identity.
I can't decide if Aristotle made an error of if he was a genius.
Although these questions were likely long before Aristotle, his own contribution was more specifically about a mix of quantification, static propositions or nouns and a predicate of existence. So it was not as expansive as using 'classics' of the 1800s with George Boole's take. His take on it was incredible for its day though and it covers enough of most everyday conversations.

I believe from the context of the Judaeo-Christian Bibles and related books that they probably though of all of this but labelled the unknown variable sources as having an extension of human-like qualities, like gods. This is too much of a digression but I think that the ancient ancients had already thought of these questions but we get them now as 'myths' about literal 'gods' rather than variables unknown. [we don't give them much the credit they likely deserved. I'm guessing that the dark ages were about the fear of this very problem's impact upon the general population.
Scott Mayers wrote:
Wed Feb 27, 2019 1:10 am
Assigning 0 to (A == A) is equivalent to assigning 0 == 1 in a way that one might say, "From nothing, we can get something."
See! Inversion! :)

Eventually you start questioning those damn "laws" and you begin to contradict THEM out of our own mind.
And you emerge on the other side with intuitionistic logic.

The laws are like training wheels until you can learn to think :)
And then you can take off the training wheels yourself.

I am going to finish responding to the rest of your post in the morning. It's 2am. My brain scanned over it and said "cannot compute".
So you are returning to the nothing? We'll have to wait until you become one again. :lol:

surreptitious57
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 3:18 am

Scott Mayers wrote:
( I ) Can we find some universal logic that can cover the full range of all specific logical systems ?

( 2 ) Are we permitted to use any logic especially some possible universal one with initial simple premises
( including possibly none ) to prove all of reality beyond mere abstraction such as scientific truths ?
The notion of a universal logic is flawed because universal knowledge applied to any discipline is simply not possible
Knowledge by definition has to be a posteriori but science is inductive so its knowledge base can never be complete
No logical system outside of science could absolutely prove it for this very reason but could do so if it was deductive

Logik
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by Logik » Wed Feb 27, 2019 8:55 am

surreptitious57 wrote:
Wed Feb 27, 2019 2:08 am
Logic is the foundation of both philosophy and mathematics but they are also separate disciplines
Computer science is a branch of both mathematics and science which are also separate disciplines
I will accept your premises as valid for now, simply so that I can help you unify these concepts into one.

What is the foundation of logic?

Grammar and semantics. The rules for forming coherent, consistent and meaningful thoughts.
These coherent thoughts are then expressed through language.

Every unique set of "rules for forming coherent, consistent and meaningful thoughts" a new language/logic makes.
Since you can have a near-infinite set of rules. And a near-infinite set of rule permutations - you can have near-infinite languages (this is what Postmodern philosophers have been on about. This is what Derida's means by "il n'y a pas de hors-texte" .

It alludes to the fact that text, symbols, squiggles and characters contain absolutely no meaning without knowing the grammar, semantics and most importantly - the INTENTION of the person who expressed any particular thought into language/logic/mathematics.

In the simplest term possible: in a universe where you are free to invent an near-infinite number of languages - what are the odds that any two people speak the EXACT same language? But I am getting a little off-topic.

Back to near-infinite number of languages. How do we enumerate ALL of them?

https://en.wikipedia.org/wiki/Chomsky_h ... 0_grammars
Type-0 grammars include all formal grammars. They generate exactly all languages that can be recognized by a Turing machine.
Turing machines are the foundational concept of Computer Science.

Now that we have unpacked all the things to the bottom. We have established these two truths:

Turing machines are computers.
Grammar is foundational of language.

Now follow my finger up to the surface.

Turing machines can enumerate ALL Type-0 formal grammars: logic, mathematics, programming languages!
You brain is a Turing machine.

Understanding how your mind works is computer science. Once you understand your mind. All languages can be unified.

surreptitious57
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 9:38 am

I agree that your brain is a Turing machine however it is not exclusively so only sometimes
We think emotionally as well as logically unlike actual machines which only think logically

Logik
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by Logik » Wed Feb 27, 2019 10:22 am

surreptitious57 wrote:
Wed Feb 27, 2019 9:38 am
I agree that your brain is a Turing machine however it is not exclusively so only sometimes
We think emotionally as well as logically unlike actual machines which only think logically
What is emotion? Is it not information?

It's a feedback loop from your body to CPU that something requires attention.
https://en.wikipedia.org/wiki/Interrupt

Our brains are a bunch of systems working together as a team. Sometimes even a janitors requires the full, undivided attention of the CEO.
Feed back loops :)

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

surreptitious57
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 10:58 am

Emotion is information but information is not always knowledge so will not always make sense
There is in actual fact no requirement for ANY emotion to be rigorous / consistent like logic is

Logik
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by Logik » Wed Feb 27, 2019 11:09 am

surreptitious57 wrote:
Wed Feb 27, 2019 10:58 am
Emotion is information but information is not always knowledge so will not always make sense
There is in actual fact no requirement for ANY emotion to be rigorous / consistent like logic is
So? Know thyself :)

The colloquial term for this is EQ - emotional intelligence. It's a scientific process like any other - it starts with observation first.

We, men are somewhat disadvantaged in this department unlike women. It comes much more naturally and instinctive to them than it comes to us. Because their emotions ring louder bells in their brains than in ours. So you know - they are forced to listen. Men just go "shut up! I am busy now."

Introspection goes a long way to addressing this, but if you want to set yourself up for success then nothing brings about compound interest in returns like having a loving and emotionally intelligent woman in your life who can set you straight whey you fall astray.

(DON'T tell my fiance I said that - I am STILL pretending she is not in control)

surreptitious57
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by surreptitious57 » Wed Feb 27, 2019 12:12 pm

Peace of mind for me is being as detached as possible both physically and psychologically
Having a woman around me would disturb this balance and so I prefer to be alone instead

Logik
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Re: What the theorems of Incompleteness or Undecidability assert...

Post by Logik » Wed Feb 27, 2019 12:16 pm

surreptitious57 wrote:
Wed Feb 27, 2019 12:12 pm
Peace of mind for me is being as detached as possible both physically and psychologically
Having a woman around me would disturb this balance and so I prefer to be alone instead
Who are you trying to convince? Me or yourself :)

"physical and psychological detachment" is an overly-sophisticated way of describing death.

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