## The limitations of Aristotelian logic:LOGIC/ESSENCE AND LANGUAGE LEAD TO THE MEANINGLESSNESS OF ALL VIEWS

### The limitations of Aristotelian logic:LOGIC/ESSENCE AND LANGUAGE LEAD TO THE MEANINGLESSNESS OF ALL VIEWS

THE LIMITATIONS OF ARISTOTELIAN LOGIC

THE END OF ARISTOTELIAN LOGIC

LOGIC/ESSENCE AND LANGUAGE LEAD TO THE

MEANINGLESSNESS OF ALL VIEWS

http://gamahucherpress.yellowgum.com/wp ... smbook.pdf

THE END OF ARISTOTELIAN LOGIC

LOGIC/ESSENCE AND LANGUAGE LEAD TO THE

MEANINGLESSNESS OF ALL VIEWS

http://gamahucherpress.yellowgum.com/wp ... smbook.pdf

### Re: The limitations of Aristotelian logic:LOGIC/ESSENCE AND LANGUAGE LEAD TO THE MEANINGLESSNESS OF ALL VIEWS

Here is an explanation why. "=" means EVERYTHING. Quite literally.

The Mathematical fraternity currently draws a distinction between the notions of provability and decidability.

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

https://en.wikipedia.org/wiki/Decidability_(logic)

All 'proofs' of **x = x** are axiomatic from the Classic identity. Even the Mathematical theorem prover Coq behaves this way.

From the Curry-Howard isomorphism proofs are isomorphic to computer programs: https://en.wikipedia.org/wiki/Curry%E2% ... espondence

In order to get to where I am I have junked Set Theory and started with Type Theory as fundamental to all Mathematics. https://en.wikipedia.org/wiki/Type_theory

In the universe of Type Theory. The Human universe 1 is not anything in particular. 1 is just a symbol. It means whatever you want it to mean.

The string 1 represents the integer 1, but what does the integer 1 mean?

In the abstract, and when given infinite amount of time and memory the Turing Machine will indeed determine that for all x: x = x.

The problem in a physical reality is that computation requires non-zero amount of energy, and non-zero number of operations in order to decide on the truth-value of a proposition. Even a proposition as simple as 'x = x' needs to be computed/decided from 1st principles. To conclude it axiomatically from Classical identity simply assumes truth. What does 1 mean?!? To a Mathematician - nothing. To a Physicist - everything!

It's information/meaning. It is the whole universe!

Classical logic conflates the notions of **identity** and **value**.

On a Turing machine **Identity** means unique memory address. Lets call it M.

**Value** means contents-of-memory at location M. Lets call it VALUE(M).

### Drawing a distinction between identity and value

Identity := id(x)

Value := value(x)

P1. for all x: id(x) == value(x) => False

The identity of an object is not the same as its value. We will use Big-O notation to quantify 'value' https://en.wikipedia.org/wiki/Big_O_notation

For those unfamiliar with algorithmic analysis and Big-O notation, suffice to say that it is synonymous with the English notion of complexity.

A simple thing is O(1). An infinitely complex thing is O(∞). Complexity is a function of value.

The more value (information, matter) an object contains - the more complex it is.

### The law of identity in a Digital Physics universe.

P2.A for all x: id(x) == id(x) => True

Each discernable object in physical reality has a universally unique identity.

The computational cost of the id(x) function is O(1).

Telling that two things are not the same is trivial! That is literally why we say 'two things'.

### The law of value in the Digital Physics universe (Classical law of identity)

The more information an object contains - the harder it is to decide its value. The harder it becomes to prove "x == x".

The cost of the decision is O(1) for small values of X (e.g really simple objects) and O(∞) for infinite values of X e.g really complex objects.

P3. for all x: x == x => UNDECIDABLE, Best case: O(1), Worse case: O(∞)

Aristotelian Identity is the principle of explosion in disguise! For infinitely complex things it is impossible to decide on their value.

Our universe may not be infinite, but it is incredibly complex.

### Implications

The Classical law of identity is an illusion. It causes us to mistake the complex for the simple. Behind a simple statement like "x = x" hides infinite amount of complexity and meaning. This very fact prevents us from saying anything useful about the integers beyond phenomenology. If I can't recognize an integer for what it is then I am stuck in a dream.

The solution: x = x must be proved. And it can't be proven for infinities.

The Mathematical fraternity currently draws a distinction between the notions of provability and decidability.

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

https://en.wikipedia.org/wiki/Decidability_(logic)

All 'proofs' of **x = x** are axiomatic from the Classic identity. Even the Mathematical theorem prover Coq behaves this way.

From the Curry-Howard isomorphism proofs are isomorphic to computer programs: https://en.wikipedia.org/wiki/Curry%E2% ... espondence

In order to get to where I am I have junked Set Theory and started with Type Theory as fundamental to all Mathematics. https://en.wikipedia.org/wiki/Type_theory

In the universe of Type Theory. The Human universe 1 is not anything in particular. 1 is just a symbol. It means whatever you want it to mean.

The string 1 represents the integer 1, but what does the integer 1 mean?

In the abstract, and when given infinite amount of time and memory the Turing Machine will indeed determine that for all x: x = x.

The problem in a physical reality is that computation requires non-zero amount of energy, and non-zero number of operations in order to decide on the truth-value of a proposition. Even a proposition as simple as 'x = x' needs to be computed/decided from 1st principles. To conclude it axiomatically from Classical identity simply assumes truth. What does 1 mean?!? To a Mathematician - nothing. To a Physicist - everything!

It's information/meaning. It is the whole universe!

Classical logic conflates the notions of **identity** and **value**.

On a Turing machine **Identity** means unique memory address. Lets call it M.

**Value** means contents-of-memory at location M. Lets call it VALUE(M).

### Drawing a distinction between identity and value

Identity := id(x)

Value := value(x)

P1. for all x: id(x) == value(x) => False

The identity of an object is not the same as its value. We will use Big-O notation to quantify 'value' https://en.wikipedia.org/wiki/Big_O_notation

For those unfamiliar with algorithmic analysis and Big-O notation, suffice to say that it is synonymous with the English notion of complexity.

A simple thing is O(1). An infinitely complex thing is O(∞). Complexity is a function of value.

The more value (information, matter) an object contains - the more complex it is.

### The law of identity in a Digital Physics universe.

P2.A for all x: id(x) == id(x) => True

Each discernable object in physical reality has a universally unique identity.

The computational cost of the id(x) function is O(1).

Telling that two things are not the same is trivial! That is literally why we say 'two things'.

### The law of value in the Digital Physics universe (Classical law of identity)

The more information an object contains - the harder it is to decide its value. The harder it becomes to prove "x == x".

The cost of the decision is O(1) for small values of X (e.g really simple objects) and O(∞) for infinite values of X e.g really complex objects.

P3. for all x: x == x => UNDECIDABLE, Best case: O(1), Worse case: O(∞)

Aristotelian Identity is the principle of explosion in disguise! For infinitely complex things it is impossible to decide on their value.

Our universe may not be infinite, but it is incredibly complex.

### Implications

The Classical law of identity is an illusion. It causes us to mistake the complex for the simple. Behind a simple statement like "x = x" hides infinite amount of complexity and meaning. This very fact prevents us from saying anything useful about the integers beyond phenomenology. If I can't recognize an integer for what it is then I am stuck in a dream.

The solution: x = x must be proved. And it can't be proven for infinities.

Last edited by Logik on Sat Mar 02, 2019 6:18 pm, edited 1 time in total.

### Re: The limitations of Aristotelian logic:LOGIC/ESSENCE AND LANGUAGE LEAD TO THE MEANINGLESSNESS OF ALL VIEWS

Dean has already pointed that out in 2002 go read the link to seeThe Classical law of identity is an illusion

### Re: The limitations of Aristotelian logic:LOGIC/ESSENCE AND LANGUAGE LEAD TO THE MEANINGLESSNESS OF ALL VIEWS

I am sure he did. I am giving you a technical how/why + a fix.

Here's a proof-of-concept on how to prove the integers and assign a value to them (meaning)

https://repl.it/@LogikLogicus/INTEGERS

I am sure he did. I am giving you a technical how/why + a fix

thanks

thanks

So, this is some scary stuff...

Automated theorem proving is a thing in Mathematics now. Lots of Mathematicians building software that does what they want it to do without knowing anything about computation.

I spoke with a maintainer of the software and here are their words:

So the truth-value of the law of identity cannot be decided. HILARIOUS.

Coq is inconsistent. Classical logic is inconsistent.

Proofs compute! Proofs are decidable. To ignore decidability is to reject Information Theory.

Automated theorem proving is a thing in Mathematics now. Lots of Mathematicians building software that does what they want it to do without knowing anything about computation.

I spoke with a maintainer of the software and here are their words:

The computational complexity of x = x is O(∞) for x -> ∞ can you spell Halting Poblem!you use Coq's equality type "x = x" is a theorem for any x of any type, but that does not mean that equality is decidable, only provable.

You wouldn't be able to write a decidable equality test for an infinite stream of bits.

Decidable <> Provable

So the truth-value of the law of identity cannot be decided. HILARIOUS.

Coq is inconsistent. Classical logic is inconsistent.

Proofs compute! Proofs are decidable. To ignore decidability is to reject Information Theory.

- Speakpigeon
**Posts:**964**Joined:**Sat Nov 11, 2017 3:20 pm**Location:**Paris, France, EU

THE UNIVERSALITY OF ARISTOTELIAN LOGICanne wrote: ↑Sat Mar 02, 2019 10:25 amTHE LIMITATIONS OF ARISTOTELIAN LOGIC

THE END OF ARISTOTELIAN LOGIC

LOGIC/ESSENCE AND LANGUAGE LEAD TO THE

MEANINGLESSNESS OF ALL VIEWS

http://gamahucherpress.yellowgum.com/wp ... smbook.pdf

THE ENDLESSNESS OF ARISTOTELIAN LOGIC

UNDERSTANDING LOGIC LEADS TO

A NEW METAPHYSICAL PERSPECTIVE

ON THE TOPOLOGY OF REALITY

Sorry, no supporting link here.

EB

And what is a proof without reverting to P=P?Logik wrote: ↑Sat Mar 02, 2019 6:58 pmSo, this is some scary stuff...

Automated theorem proving is a thing in Mathematics now. Lots of Mathematicians building software that does what they want it to do without knowing anything about computation.

I spoke with a maintainer of the software and here are their words:

The computational complexity of x = x is O(∞) for x -> ∞ can you spell Halting Poblem!you use Coq's equality type "x = x" is a theorem for any x of any type, but that does not mean that equality is decidable, only provable.

You wouldn't be able to write a decidable equality test for an infinite stream of bits.

Decidable <> Provable

So the truth-value of the law of identity cannot be decided. HILARIOUS.

Coq is inconsistent. Classical logic is inconsistent.

Proofs compute! Proofs are decidable. To ignore decidability is to reject Information Theory.

ASSUMING P=P is the very problem!

You need to ASSERT P=P.

You need to write the algorithm which does it. You need to define the function: equal(x,y) =>

And you need to use that function to assert equal(P,P)

As I explained - you HAVE to pay the piper.

Asserting 1 = 1 is cheap.

Asserting 555555555555555555555555555551 = 55555555555555555555555555551 is NOT cheap.

You have to DO THE WORK.

Already did.Logik wrote: ↑Fri Mar 08, 2019 5:03 amASSUMING P=P is the very problem!

You need to ASSERT P=P.

You need to write the algorithm which does it. You need to define the function: equal(x,y) =>

And you need to use that function to assert equal(P,P)

As I explained - you HAVE to pay the piper.

Asserting 1 = 1 is cheap.

Asserting 555555555555555555555555555551 = 55555555555555555555555555551 is NOT cheap.

You have to DO THE WORK.

"Px"

Or (Noun/Verb, passive/active, etc.) exist simultaneously still allows for aristotelian identity properties under:

PxP

xPx

Argued in other threads.

Proofs compute...yes, however this does not negate the law of identity as the computing proof still requires the proof effectively as a boundary of "movement" (in this case computation as the separation and connection of variables).

For example:

Red is proved, as a quality, through its continual variation under multiple "reds" as a quality composed of degrees. The degree, as a finite phenomenon, still necessitates movement where a continual progression inherently linked to multiplicity observes it as dynamic.

In simpler terms the degree exists through a progression to other degrees, hence is an observed of movement where one part inverts to another.

The proof effectively computes by inverting to other "proofs" where the proof itself, as computing, is still subject to a law of identity on the respect it exists as a point of inversion. It exists as an individuator; and as an individuator the proof maintains aristotelian properties of identity because it replicates.

Aristotelian identity properties are recursive in nature, that is what grounds identity: recurssion.

Lip service.Eodnhoj7 wrote: ↑Fri Mar 08, 2019 5:31 amAlready did.

"Px"

Or (Noun/Verb, passive/active, etc.) exist simultaneously still allows for aristotelian identity properties under:

PxP

xPx

Argued in other threads.

Proofs compute...yes, however this does not negate the law of identity as the computing proof still requires the proof effectively as a boundary of "movement" (in this case computation as the separation and connection of variables).

For example:

Red is proved, as a quality, through its continual variation under multiple "reds" as a quality composed of degrees. The degree, as a finite phenomenon, still necessitates movement where a continual progression inherently linked to multiplicity observes it as dynamic.

In simpler terms the degree exists through a progression to other degrees, hence is an observed of movement where one part inverts to another.

The proof effectively computes by inverting to other "proofs" where the proof itself, as computing, is still subject to a law of identity on the respect it exists as a point of inversion. It exists as an individuator; and as an individuator the proof maintains aristotelian properties of identity because it replicates.

Aristotelian identity properties are recursive in nature, that is what grounds identity: recurssion.

What you failed to spot in between the linguistic/philosophical masturbation is that:

1 = 1 => True

555555555555555555555555555551 = 55555555555555555555555555551 => False

In order to ASSERT truth or falsity.....

YOU HAVE TO DO THE WORK

Save the insults, you program little boxes and convince other's that sending a picture of a curve is worth all the effort...stick with what you do best.Logik wrote: ↑Fri Mar 08, 2019 5:33 amLip service.Eodnhoj7 wrote: ↑Fri Mar 08, 2019 5:31 amAlready did.

"Px"

Or (Noun/Verb, passive/active, etc.) exist simultaneously still allows for aristotelian identity properties under:

PxP

xPx

Argued in other threads.

Proofs compute...yes, however this does not negate the law of identity as the computing proof still requires the proof effectively as a boundary of "movement" (in this case computation as the separation and connection of variables).

For example:

Red is proved, as a quality, through its continual variation under multiple "reds" as a quality composed of degrees. The degree, as a finite phenomenon, still necessitates movement where a continual progression inherently linked to multiplicity observes it as dynamic.

In simpler terms the degree exists through a progression to other degrees, hence is an observed of movement where one part inverts to another.

The proof effectively computes by inverting to other "proofs" where the proof itself, as computing, is still subject to a law of identity on the respect it exists as a point of inversion. It exists as an individuator; and as an individuator the proof maintains aristotelian properties of identity because it replicates.

Aristotelian identity properties are recursive in nature, that is what grounds identity: recurssion.

What you failed to spot in between the linguistic/philosophical masturbation is that:

1 = 1 => True

555555555555555555555555555551 = 55555555555555555555555555551 => False

In order to ASSERT truth or falsity.....

YOU HAVE TO DO THE WORK

False you are using the principle of explosion like a kid in a toy.

Of course you can get it to be false.

P=P is false unless =P= is observed to balance it out (where "P" is defined in the first point, but not "=" and the inverse in the second point).

So P=P is both true and false depending on context.

=P= is both true and false depending on comtext

P= exists as is where it is true through the cycling of P=P and =P=.

Where one is false the other is true through P=

You have a knack for over-complicating the simple and over-simplifying the complex.Eodnhoj7 wrote: ↑Fri Mar 08, 2019 5:45 amSave the insults, you program little boxes and convince other's that sending a picture of a curve is worth all the effort...stick with what you do best.

False you are using the principle of explosion like a kid in a toy.

Of course you can get it to be false.

P=P is false unless =P= is observed to balance it out (where "P" is defined in the first point, but not "=" and the inverse in the second point).

So P=P is both true and false depending on context.

=P= is both true and false depending on comtext

P= exists as is where it is true through the cycling of P=P and =P=.

Where one is false the other is true through P=

555555555555555555555555555551 = 55555555555555555555555555551

The number on the left contains 30 digits in total.

The number on th right contains 29 digits in total.

The statement 555555555555555555555555555551 > 55555555555555555555555555551 is True

I tricked you. I guessed (correctly) that you are probably not going to count the number of digits. Because you are a lazy thinker.

Principle of least effort strikes again.

If you had done the WORK to actually compare them....

Actually far from it, I already observed the number of digits can be equal and still result in a relative true or false statement...and still be logical. I could care less whether the number is the same or not when both points can be over routed entirely.Logik wrote: ↑Fri Mar 08, 2019 5:56 amYou have a knack for over-complicating the simple and over-simplifying the complex.Eodnhoj7 wrote: ↑Fri Mar 08, 2019 5:45 amSave the insults, you program little boxes and convince other's that sending a picture of a curve is worth all the effort...stick with what you do best.

False you are using the principle of explosion like a kid in a toy.

Of course you can get it to be false.

P=P is false unless =P= is observed to balance it out (where "P" is defined in the first point, but not "=" and the inverse in the second point).

So P=P is both true and false depending on context.

=P= is both true and false depending on comtext

P= exists as is where it is true through the cycling of P=P and =P=.

Where one is false the other is true through P=

555555555555555555555555555551 = 55555555555555555555555555551

The number on the left contains 30 digits in total.

The number on th right contains 29 digits in total.

The statement 555555555555555555555555555551 > 55555555555555555555555555551 is True

I tricked you. I guessed (correctly) that you are probably not going to count the number of digits. Because you are a lazy thinker.

Principle of least effort strikes again.

If you had done the WORK to actually compare them....

Your point is mute either way.

If you have to resort to card shuffling tricks then obviously you are the sophist you complain everyone of being.

Philosophy is not for you...you are trapped within the contradictory language of python and won't get out because you are nothing without it.

Go program a care bear picture and email it to a poor Chinese kid...then tell yourself about how you serve the community.

Card-shuffling trick? The numbers are right there for you to see. The identity was right there for you to evaluate.

By NOT doing the work you fooled yourself.

The first principle is that you must not fool yourself – and you are the easiest person to fool. -- Richard Feynman

Before you can "get out" - first you have to figure out what box you are stuck in.... Your box is philosophy.

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